Centrality Measures

Terrorist attacks keep happening around the world, which has led researchers to use Social Network Analysis (SNA) as a way to study terrorism. Terrorist groups function like secretive networks, strengthening their operations while staying hidden. This study introduces a new approach to reveal and break apart such networks by using four different centrality measures. First, the method predict hidden or missing link in the network using these centrality measures. Then, the network is dismantled by applying the Galton-Watson extinction probability model, which helps estimate the chances of the network collapsing. The study looks at real-world cases, such as the 9/11 terrorist attacks and the M-19 group, to test how well link prediction works. It shows that removing the most influential members (highly ranked nodes) is essential for weakening and destroying a terrorist network. Additionally, the research examines how dangerous the network is (lethality) and how tightly connected its members are (bonding), since cohesiveness is critical for a network's survival. The results demonstrate that link prediction is a key tool for exposing hidden terrorist networks, making it an important strategy for counterterrorism efforts.

This study has used network measures to classify the children interactions in playground. The variance of network processes between genders was tested. Five girls and boys (n = 10; 4.6 0.6 years old) were observed. Statistical procedures has revealed significant differences between genders in IDC (p = 0.027; ES = 0.476; moderate effect) and BC (p = 0.011; ES = 0.576; moderate effect). Results revealed a greater cooperation process between boys.

The aim of the present study is the scientometric analysis of research in the field of child and adolescent clinical psychology that has been indexed in the Web of Science citation database; in addition, the co-authorship network of countries has also been evaluated and visualized based on the theory of structural holes. The present applied and quantitative research was conducted in a descriptive method using scientometric indicators and network analysis. The study's statistical population was 800 documents related to child and adolescent clinical psychology in the Web of Science citation database. The present study used VOSviewer software to draw the co-authorship network of researchers and countries, Spss software for statistical aspects, and Pajek software to draw structural holes. Based on the findings, the Spearman correlation test (P<0.000, r=0.140) showed a positive and significant relationship between the number of researchers' documents and the number of citations they received; also, the results of the Spearman correlation test (P<0.000, r=0.785) indicated a positive and significant relationship between the number of documents of countries and their number of citations. Additionally, the co-authorship network of researchers and countries was drawn to show the core elements of the network. In terms of the number of received citations, the countries of the United States, the United Kingdom, and Australia ranked first to third, respectively. In terms of the number of documents, the countries of the United States, Italy, and the United Kingdom ranked first to third, respectively. In addition, in the co-authorship network of the studied documents, countries that filled the structural gaps between countries were identified, and the three countries of the United States, Germany, and Spain ranked first to third.

This paper presents a novel graph neural network (GNN)-based model for personalized learning with advanced graph neural networks, incorporating both graph convolutional networks (GCN) and graph attention Networks (GAT). Our model leverages GCN, which consists of multiple layers embedding deep learning models, to aggregate data from neighboring nodes and capture the intricate relationships between students and courses. The GAT layers refine these embeddings by dynamically assigning importance weights to connections, prioritizing relationships critical for personalized course recommendations. This dual-layered approach enables the model to account for both global structural patterns and locally significant interactions within the student-course graph. We evaluated the performance of our model using the open university learning analytics dataset (OULAD), a rich dataset encompassing student demographic information, interaction data, and course performance metrics. Experimental results achieved 78.9% F1-score, 78.3% precision, and 76.2% recall in personalized recommendations, outperforming single-layer GCN implementations by approximately 15 percentage points. These results demonstrate the model's ability to handle complex, dynamic relationships in educational data, ensuring more relevant and effective recommendations. By addressing key challenges in recommendation systems, such as the need for dynamic weighting of relationships and the handling of sparsity in educational data, our study underscores the transformative potential of GNNs in advancing personalized education. This work sets the stage for further exploration of GNN applications in e-learning, paving the way for adaptive and intelligent course recommendation systems that align with individual learning needs and preferences.

Influential spreaders are used to maximize or control the
spreading dynamics in a network. It acts as a maximizer in the case
of information dissemination and a controller to control the epidemic
spreading. In the literature, researchers are mostly focused on finding
the best spreader from an undirected network. Indeed, the edge’s di-
rection of a spreading process in the network has immense significance
while estimating the influential spreaders. This paper presents a novel
method, i.e., the ”crossbred method” to identify the best spreaders for a
directed network. The proposed method considers the spreading proper-
ties of the directed network. It takes account of two popular parameters
of a spreading process, i.e., node’s out-degree and spreading’s reachabil-
ity of an originator node. We have verified the spreading performance of
the proposed method with the Directed Susceptible-Infected-Recovered
(SIR) spreading epidemic model on six real networks. The outcome of
the investigation demonstrates that the proposed method achieved sig-
nificant improvement in terms of spreading dynamics over the existing
methods of directed networks such as out-degree centrality, betweenness
centrality, pagerank centrality, eigenvector centrality, cluster-rank cen-
trality, outgoing closeness centrality, hybrid centrality.

A Base Nacional Curricular Comum (BNCC) é o documento normativo para a elaboração dos currículos escolares nos respectivos sistemas educacionais em atendimento ao que determina a Lei de Diretrizes e Bases da Educação Nacional (LDBEN). As definições apresentadas na BNCC abrangem toda a Educação Básica desde a Educação Infantil ao Ensino Médio. Para a presente pesquisa delimita-se a parte do Ensino Fundamental (EF), Anos Finais, ou seja, do 6º ao 9º Anos e, tendo como objeto de estudo o componente curricular de Geografia. Nesse foco disciplinar, além das competências da área das Ciências Humanas e do componente curricular Geografia a BNCC apresenta o detalhamento por Ano/componente curricular do que denomina unidades temáticas, objetos de conhecimento e habilidades. São definições orientadoras, mas não suficientes para a efetivação do ensino-aprendizagem na sala de aula. É preciso completar os elementos didáticos necessários para possibilitar os percursos escolares de apropriação das habilidades e construção das competências informativas e formativas aí definidas. Essa a questão remete para a necessidade de compreensão do método da ciência geográfica e, de compreensão sobre a Didática específica da Geografia Escolar. Como fazer acontecer esse percurso é a questão que identifica o problema de pesquisa. Para isso acontecer, o projeto propõe movimentar, mobilizar, navegar nesse território ainda movediço, construir o objeto, desenvolver ações investigativas com a perspectiva de apropriação de saberes necessários para qualificar a análise e elaborar proposições didáticas. Projetam-se então ações ou focos de estudos para identificar, organizar, interpretar esse conjunto de definições, da habilidade à competência, passando pelos objetos de conhecimento e pelas unidades temáticas. Compreender como interagem nesse citado percurso as concepções de método da ciência geográfica e da Didática (específica) da Geografia, compreender sobre o papel do livro didático ou de outros recursos didáticos virtuais e, ainda, como ficam os espaços de atuação e de criação didática dos professores constituem objetos de investigação a serem perseguidos. Identificar e compreender o que muda e o que não muda com a BNCC e, se essas mudanças estão determinadas ou os sujeitos podem em qual medida serem protagonistas do ensino-aprendizagem. Elaborar essas interpretações serão essenciais para subsidiar as elaborações didáticas para o desenvolvimento com qualidade do ensino-aprendizagem da Geografia Escolar.

In response to the dynamic and ever-evolving landscape of network attacks and cybersecurity, this study aims to enhance network security by identifying critical nodes and optimizing resource allocation within budget constraints. We introduce a novel approach leveraging node centrality scores from four widely-recognized centrality measures. Our unique contribution lies in converting these centrality metrics into actionable insights for identifying network attack probabilities, providing an unconventional yet effective method to bolster network robustness. Additionally, we propose a closed-form expression correlating network robustness with node-centric features, including importance scores and attack probabilities. At the core of our approach lies the development of a nonlinear optimization model that integrates predictive insights into node attack likelihood. Through this framework, we successfully determine an optimal resource allocation strategy, minimizing cyberattack risks on critical nodes while maximizing network robustness. Numerical results validate our approach, offering further insights into network dynamics and improved resilience against emerging cybersecurity threats.

Christopher Alexander has presented key concepts, such as wholeness, centres, and harmony-seeking computations, related to the coherence reached by a system. Wholeness is the global structural character of a given configuration existing in space. According to Alexander, wholeness is measurable although we do not have a mathematical language to describe it yet. Some authors have proposed a network perspective to address this problem. However, it is still poorly developed. This paper discusses how to improve the network approach already suggested in the literature. The aim is contributing to the debate on how to operationalise Alexander’s theories through a network perspective. We check out different descriptive systems and different centrality measures, which can be used to reveal the spatial relationship between urban entities and its hierarchy. The main conclusion is that centrality measures seem to offer an opportunity to get closer to Alexander’s concepts. However, a key point to...

Twitter is one of the most popular social networking platforms that people use to communicate and interact. Organisations and companies use Twitter, as well as other social media platforms, for the marketing of their products or services. To achieve this goal they seek to partner with influential Twitter users, as a part of their influencer marketing strategy. Influencer marketing is considered more effective than traditional marketing. Influencers are more trustworthy than a business due to the fact that they have developed close connection with their followers. This marketing trend has played an important role in the rise of fake influencers in Twitter. Fake influencers inflate their follower counts by buying fake Twitter accounts from vendors and they manage to partner with companies. However, that partnership does not benefit companies as the influencer's engagement is fake. In this paper we analyse centrality and overall network characterization measures applied on Twitter fake influencer accounts and on legitimate influencer accounts. The results showed that the measures we propose are statistically significant and can be easily applied to automatically detect fake influencers on Twitter.

Twitter is one of the most popular social networking platforms that people use to communicate and interact. Organisations and companies use Twitter, as well as other social media platforms, for the marketing of their products or services. To achieve this goal they seek to partner with influential Twitter users, as a part of their influencer marketing strategy. Influencer marketing is considered more effective than traditional marketing. Influencers are more trustworthy than a business due to the fact that they have developed close connection with their followers. This marketing trend has played an important role in the rise of fake influencers in Twitter. Fake influencers inflate their follower counts by buying fake Twitter accounts from vendors and they manage to partner with companies. However, that partnership does not benefit companies as the influencer's engagement is fake. In this paper we analyse centrality and overall network characterization measures applied on Twitter fake influencer accounts and on legitimate influencer accounts. The results showed that the measures we propose are statistically significant and can be easily applied to automatically detect fake influencers on Twitter.

Graph representation learning (GRL) methods, such as graph neural networks and graph transformer models, have been successfully used to analyze graph-structured data, mainly focusing on node classification and link prediction tasks. However, the existing studies mostly only consider local connectivity while ignoring long-range connectivity and the roles of nodes. In this paper, we propose Unified Graph Transformer Networks (UGT) that effectively integrate local and global structural information into fixed-length vector representations. First, UGT learns local structure by identifying the local sub-structures and aggregating features of the k-hop neighborhoods of each node. Second, we construct virtual edges, bridging distant nodes with structural similarity to capture the long-range dependencies. Third, UGT learns unified representations through self-attention, encoding structural distance and p-step transition probability between node pairs. Furthermore, we propose a self-supervised learning task that effectively learns transition probability to fuse local and global structural features, which could then be transferred to other downstream tasks. Experimental results on real-world benchmark datasets over various downstream tasks showed that UGT significantly outperformed baselines that consist of state-of-the-art models. In addition, UGT reaches the third-order Weisfeiler-Lehman power to distinguish non-isomorphic graph pairs.

The present study was conducted with the aim of analyzing the structure of the social network of co-authoring books by faculty members in the area of educational sciences of Tehran province universities. In this research, the scientometric approach and analysis of social networks has been used. The statistical population of this research is the books published by the faculty members in the area of educational sciences in public universities of Tehran, which were published by publishing organizations and were indexed on Khaneh Ketab website. 643 books were studied using the available sample method. In this research, at first the patterns of co-authorship in the books of faculty members in the area of educational sciences were examined, then, with a scientometric approach, the structure of the co-authorship networks using macro indicators of density including clustering coefficient, network diameter, connectivity, and average were studied. The distance was considered and micro-indices of centrality degree, betweenness, closeness and eigenvector were used to check the performance of each member. Examining the patterns of co-authorship among faculty members showed that the highest amount of co-authorship among the studied population was 231 cases of double authorship (36 percent), 104 cases of triple authorships (16 percent), 32 cases of four authorships (5 percent), and 46 cases of five authorships or more (7 percent). The share of single authorship has been reported in 230 cases (36 percent). In other words, 64 percent of the books are collaboratively published. The co-authoring network of books by faculty members in the area of educational sciences consists of 106 nodes and 100 links. Also, the examination of the macro indicators of the social network of co-authorship in the studied society shows that this structure has low cohesion due to its low density, and the network of co-authorship of books by educational science faculty members is a discrete network with very few relationships between different nodes. The analysis of the micro-indices show that according to the centrality index, scholars such as Mahmoud Mehrmohammadi, Kourosh Fathi Vajargah, Mohammad Attaran and Khosrow Bagheri have prominent positions and their level of influence and power in the network is higher than other members. Also, these people somehow control the flow of information in the network.

Christopher Alexander has presented key concepts, such as wholeness, centres, and harmony-seeking computations, related to the coherence reached by a system. Wholeness is the global structural character of a given configuration existing in space. According to Alexander, wholeness is measurable although we do not have a mathematical language to describe it yet. Some authors have proposed a network perspective to address this problem. However, it is still poorly developed. This paper discusses how to improve the network approach already suggested in the literature. The aim is contributing to the debate on how to operationalise Alexander’s theories through a network perspective. We check out different descriptive systems and different centrality measures, which can be used to reveal the spatial relationship between urban entities and its hierarchy. The main conclusion is that centrality measures seem to offer an opportunity to get closer to Alexander’s concepts. However, a key point to...

This article aims to measure the relationship between metrics of visibility and bookmarking in social platforms (Citeulike, Mendeley and Figshare) with citation counts in Scopus, Web of Science, PubMed central and Crossref. This study is original in terms of its objective, and the data gathering scheme is descriptive of correlation type with a citation analysis approach. The population in this study consists of 90,728 research papers published in PLOS between 2009 and 2013. A sample of 1892 was chosen based on Cochran formula. The results showed that the visibility, Citeulike and Mendeley bookmarking counts have significant positive correlation with citations in all of the investigated systems. Conversely, social bookmarking counts on Figshare showed significant negative correlation with citations. Visibility metric has significant positive correlation with bookmarking counts in Citeulike and Mendeley, while it does not correlate with social bookmarking metric in Figshare. The results of this study suggest that sharing scientific publications in social networks such as Mendeley may increase the visibility and the future citations.

This article aims to measure the relationship between metrics of visibility and bookmarking in social platforms (Citeulike, Mendeley and Figshare) with citation counts in Scopus, Web of Science, PubMed central and Crossref. This study is original in terms of its objective, and the data gathering scheme is descriptive of correlation type with a citation analysis approach. The population in this study consists of 90,728 research papers published in PLOS between 2009 and 2013. A sample of 1892 was chosen based on Cochran formula. The results showed that the visibility, Citeulike and Mendeley bookmarking counts have significant positive correlation with citations in all of the investigated systems. Conversely, social bookmarking counts on Figshare showed significant negative correlation with citations. Visibility metric has significant positive correlation with bookmarking counts in Citeulike and Mendeley, while it does not correlate with social bookmarking metric in Figshare. The resul...

Online social networks (OSNs) such as Facebook, Twitter, and Instagram have attracted many users all around the world. Based on the centrality concept, many methods are proposed in order to find influential users in an online social network. However, the performance of these methods is not always acceptable. In this paper, we proposed a new improvement on centrality measures called P-centrality measure in which the effects of node predecessors are considered. In an extended measure called EP-centrality, the effect of the preceding predecessors of node predecessors are also considered. We also defined a combination of two centrality measures called NodePower (NP) to improve the effectiveness of the proposed metrics. The performance of utilizing our proposed centrality metrics in comparison with the conventional centrality measures is evaluated by Susceptible-Infected-Recovered (SIR) model. The results showed that the proposed metrics display better performance finding influential users than normal ones due to Kendall's τ coeff icient metric.

This article studies about the collaborative measures of published documents in the field of chromosome anomalies. It discusses about inadequacies of collaborative measures in analyzing the collaborating behavior and strength of collaboration in a discipline. It also suggests centrality measures, as degree centrality, closeness, and betweenness in analyzing the collaboration among the researchers and scientists in the field of chromosome anomalies. The bibliographical database PubMed is used as sources for bibliometrics and 35912 citations examined for coauthorship pattern, collaborative behavior of the scientists. Centrality measures were used to construct a network for coauthorship in chromosome anomalies research during the year 2007-2016 and to find out the most influential predominant author in the field.

Introduction: One of the methods for evaluating scientific productions that has long received attention is citation analysis. Considering the limitations of citation analysis and the proliferation of social media and its importance in the dissemination of research results, there seems to be a need for new indicators, called altmetrics, in addition to the traditional indicators for research evaluation. Therefore, the aim of the current study is to investigate the status of articles in the field of opioid addiction using bibliometric  indicators and altmetrics, as well as to determine the relationship between the citation performance and the altmetrics performance of articles in this field.
Methods: This study is a descriptive-analytical study of an applied type, which was carried out using bibliometric and altmetrics methods. The research population includes 16,803 titles of articles in the field of opioid addiction indexed by the Scopus database from the beginning to 2022. The Scopus database and PlumX tool were used for data collection, and Excel and SPSS were used for data analysis.
Results: 80.6% of the studied publications were cited. 95% of these publications were mentioned at least once in one of the social media. The results of the research show that statistically, there is a significant and positive relationship between the number of citations and all the altmetrics.
Conclusion: Considering the positive correlation between citation and altmetrics in this study, it can be said that social media can have a positive impact on the number of citation of scientific articles. Therefore, researchers in the field of opioid addiction can use social media and share their works in various social media to get citations for their scientific activities.

Objective: This research aimed to measure the dependence and independence of documents in an Ego-centered citation network to evaluate the quality of scientific outputs in two subject areas "aerospace engineering" and "nuclear technology." Methodology: The present study is applied research and belongs to the category of scientometrics research. In the first step, the required data for creating ego-centric citation networks were extracted and stored from the Web of Science Core Collection (WOSCC) through web scraping (automated data extraction from websites) using the Mimfa Scraper (a software for automated data extraction) and the JavaScript programming language. Afterward, algorithm coding was performed in the MiMFa RAVAR DataLab, and the programming language C# was utilized to answer the research question. Findings: The research findings showed that the study conducted by Allison (2016) with 1535 citations is the most cited document in the field of nuclear technology and ranks first in terms of absolute dependence index. In comparison to the number of references in Allison's paper, 80 percent of the alters in Li's research (2018), the second most cited paper in terms of the absolute dependence index (512 citations), cited ego-related references (58 references); however, this percentage is 46 percent in Allison's paper. A study conducted by Shin has obtained the highest absolute independence index (2015 citations) compared to other highly cited articles in the field ‫شبکه‬ ‫پایش‬ ‫هسته‬ ‫فناوری‬ ‫و‬ ‫هوافضا‬ ‫مهندسی‬ ‫ایگومحور‬ ‫استنادی‬ ‫های‬ ‫ای‬ of nuclear technology. Leppanen's study (2015) ranks first in terms of the relative independence index with a score of 98 percent compared to other highly cited documents in the field of nuclear technology. Ricker (2015), along with 57 co-authors, has the highest number of citations (1542 citations) in aerospace engineering. Among these citations, 647 alters have cited the documents cited by the ego and obtained the highest absolute dependence index score. Wang's research (2020), with 52 citations, is the first paper to rank the relative independence index in the field of aerospace engineering. Conclusion: The results indicate that the level of relative dependence was higher than independence in both subject areas. Moreover, as the number of citations increases, both absolute dependence and independence increase; however, relative dependence decreases. Additionally, in recent years, the absolute dependence and independence indices have lower values than older years. However, the relative dependence index positively correlates with the year of publication. Moreover, the relative independence index positively correlates with the number of citations; its value has increased in recent years and the number of ego sources does not directly correlate with the increase in the dependence index.

1. Introduction
Considering that the goal of social science research is to train and provide skilled and specialized human resources to carry out research, education, management and planning in various social and cultural fields, and also considering that the main emphasis of this field is the education and promotion of excavations. A field about the social issues of the country and the analysis and interpretation of their roots, contexts, causes and factors, description and analysis of their extent in the society and finally the analysis of the information obtained from these studies is to solve social issues, therefore providing considered solutions to deal with them. With these problems and social developments, it is necessary. Considering that one of the evaluation criteria of universities and countries is the quantity and quality of their research outputs in international reliable databases. The status of each country's indexed research outputs in international valid indexes indicates an important part of that country's scientific activities at the international level. Therefore, in order to analyze scientific activities, a clear picture of this situation has always been the focus of the country's research managers. Therefore, it is necessary to pay attention to the quality of research outputs in Iranian universities, which are considered the most important scientific hub of the country. The results of this research can be used for planning at the level of administrations, various vice-chancellors and the entire universities under review, and by knowing the priorities, abilities and weaknesses, provide the necessary facilities to make scientific activities more targeted in the subject areas of social and behavioral sciences in the universities under review.  Therefore, this research studies and analyzes the research outputs of Iran's major universities using qualitative Scientometrics indicators in the subject areas of social and behavioral sciences during the period of 2010-2020.

Research Question
What is the status of the research outputs of Iran's major universities in the subject areas of social and behavioral sciences with a Scientometrics approach from the perspective of quantity and impact index based on Scopus database data during the years 2010 to 2020?

2. Literature Review
The review of the literature indicates that the quality of research outputs in Iran's major universities has been less studied over a long period of time and using multiple Scientometrics indicators. In most of the previous studies, only the average index and the percentage of documents were cited and the H index was used to study the quality level of research outputs. Therefore, according to the investigations carried out in the dimension of scientology and the need to pay attention to the quality of research outputs in addition to their quantity, the present article studies and analyzes the research outputs of major universities in Iran in the subject areas of social and behavioral sciences according to several indicators of effectiveness during the period of 2010-2020. In this way, it has helped to identify the scientific position of the universities in the subject areas of social and behavioral sciences, as well as planning for its development at the national level, and to help strengthen and improve the country's scientific rank at the international level.

3. Methodology
The current research is of an applied type and has been carried out with a Scientometrics approach and with documentary and citation analysis methods. The community under review is all research outputs in the subject areas of social and behavioral sciences, including "subject areas of psychology, economics (economics, econometrics and finance)", "management (business, management and accounting)", "social sciences", and "sciences", decision-making", according to the subject classification of the Scopus database, in the major universities of Iran in the years 2010 to 2020. The research implementation environment was Scopus and Scival databases. Research data was collected from March 20 to March 28, 2019 from Scopus and Scival. The method of data collection is to refer directly and get standard outputs from Scopus and Scival databases. The indicators used in this research are: citations, average citations per article, H index, weighted citation impact at the field level, percentage of highly cited articles, and percentage of articles published in top journals. Descriptive statistics (with Microsoft Excel software) were used to analyze the data.

4. Results
According to the results, the total number of research outputs in the subject areas of social and behavioral sciences of Iran's major universities in the target period was 19,582 records. In all the studied universities, the subject area of social sciences had the most research outputs. In general, the research outputs of Iran's major universities in the subject areas of social and behavioral sciences have been on the rise in the given period of time. The reason for this can be the increase of students and researchers in postgraduate studies. In terms of the number of citations index, Shahid Beheshti, Isfahan, Ferdowsi, Tabriz, and Shiraz universities have the most citations in the subject area of "social sciences" and in the universities of Tehran, Allameh Tabataba’i, and Tarbiat Modares, the subject area of "business, management and accounting" has the most citations. In most of the cases mentioned in the universities and subject areas under investigation that received the most citations, in terms of the index of highly cited articles at the threshold of 10% and the index of articles published in top journals at the threshold of 25%, they also took the highest percentages. This issue indicates the high quality of research outputs with more citations, which these findings are consistent with the vital and high research (2016) for this reason that the more the citations of the articles, the higher the quality. In terms of highly cited articles at the threshold of 10%, in the universities of Tehran, Tarbiat Modares, Isfahan, Ferdowsi, Tabriz, and Shiraz, the subject area of "Economics, Econometrics and Finance", and in Shahid Beheshti and Allameh Tabataba’i universities, the subject area of "Trade" "Management and accounting" got the highest percentages.

5. Discussion
In terms of the index of articles published in top journals at the threshold of 25%, in Shahid Beheshti, Tehran, Tarbiat Modares, Ferdowsi, Tabriz universities, in the subject area of "Business, Management and Accounting", in Allameh Tabataba’i University, in the subject area of "Psychology", in universities Isfahan and Shiraz have the highest percentages in the subject area of "Social Sciences". In this regard, it has been mentioned in most of the cases that they have obtained a high percentage in terms of the index of highly cited articles at the threshold of 10% and the index of articles published in the top journals at the threshold of 25%. This issue shows the high quality of research outputs in the mentioned subject areas, which with the research of Irfan Manesh and Hosseini (2016), in terms of the impact of general impact indicators (H index, weighted citation impact index at the field level, citations) on the increase of articles published in Top journals and highly cited articles match. Since some of the indicators examined in this research, such as citations and the number of highly cited articles, are included in some ranking systems, such as the rankings of Leiden University, Saimgo University, and Shanghai University, increasing the mentioned indicators as much as possible is effective in improving the position of universities in these ranking systems.

6. Conclusion
In general, it is very important for universities to emphasize the quality of research outputs in addition to the quantity of these outputs. Attention to the quality of research outputs with the researches of Ebrahimi and Hayati (2007), Yaminifirouz et al. (2015) and Erfanmanesh and Hosseini (2018). Considering the number of received citations of the published research outputs of Iran's major universities in the review of their performance, as well as considering the special research credit and score for the authors of highly cited articles in various subject areas can be a suitable solution in this field. Also, emphasizing the quality along with the quantity of research outputs in universities and research centers should be given special attention.

Acknowledgments
We are grateful to Shahid Beheshti University Research Vice-Chancellor for their support in the implementation of this research.

Este artigo é derivado de uma pesquisa de mestrado e explora desafios no ensino de sistemas lineares, focando a intersecção entre currículo, abordagens metodológicas e experiência de professores em serviço. O objetivo deste trabalho é conhecer as concepções, as formas de ensino e obstáculos dos docentes na abordagem de sistemas de equações lineares. A metodologia do estudo foi a Engenharia de Formação, aliada aos fundamentos da Teoria das Situações Didáticas integrados à Didática Profissional. A análise se concentra em uma Situação Didática Profissional para a abordagem do tema com o apoio do GeoGebra. A experiência dos professores destacou obstáculos no ensino, ressaltando a necessidade de estratégias pedagógicas específicas. O GeoGebra configurou-se como recurso que viabiliza uma aprendizagem visual e intuitiva, promovendo um ambiente que fomentou uma compreensão sólida e efetiva dos conceitos matemáticos.

Real-world graphs generally have only one kind of tendency in their connections. These connections are either homophily-prone or heterophilyprone. While graphs with homophily-prone edges tend to connect nodes with the same class (i.e., intra-class nodes), heterophily-prone edges tend to build relationships between nodes with different classes (i.e., inter-class nodes). Existing GNNs only take the original graph during training. The problem with this approach is that it forgets to take into consideration the "missing-half" structural information, that is, heterophily-prone topology for homophily-prone graphs and homophilyprone topology for heterophily-prone graphs. In our paper, we introduce Graph cOmplementAry Learning, namely GOAL, which consists of two components: graph complementation and complemented graph convolution. The first component finds the missing-half structural information for a given graph to complement it. The complemented graph has two sets of graphs including both homophily-and heterophily-prone topology. In the latter component, to handle complemented graphs, we design a new graph convolution from the perspective of optimisation. The experiment results show that GOAL consistently outperforms all baselines in eight real-world datasets.

The purpose of the study is to evaluate the growth or decrease of scientific output in the field of information retrieval in the Web of Science Citation Database from 2010 to 2017. The research is applied and uses scientific indices to evaluate the scientific outputs of the field of information retrieval and the statistical population includes all records of the Web of Science Citation Database. The findings showed that molar, H. was the top author in this field with 36 records, and the United States was the top country with 1984 records. The NATIONAL DELA RECHERCHE SCIENTIFIQUE CNRS Institute was recognized by producing 235 records best Institute and LECTURE NOTES IN COMPUTER SCIENCE with 915 records best Journal. Computer science was introduced as the top subject area with 8241 records. An article entitled Graph Regularized Nonnegative Matrix Factorization for Data Representation received the highest citation (including 585 citations) as the top information retrieval article. The results showed that the growth of scientific productions in the field of information retrieval did not follow a steady trend and declined during 2011-2012 as well as in 2017 and during the period of 2013 to 2016 with a growing trend in this field.

This study investigates the relationship between the measurements obtained from the social networks of ResearchGate and Academia with the scientometric indicators of Scopus and Web of Science databases. The present study is of a fundamental type that has been done in a descriptive manner and with an algorithmic approach. The statistical population of the study includes the most prolific authors in the field of Iranian Business Management who have uploaded their documents in the Scopus database between 2000-2019. 160 of these authors, who had the most documents indexed in Scopus, respectively, have been introduced as a statistical sample of the research. In order to investigate the relationship between the metrics obtained by the authors' activities in the research networks of ResearchGate and Academia with the scientometric indicators of Scopus and Web of Science databases, the statistical tests of correlation with the help of Excel and SPSS has been used. The presence and activity of Business Management writers on the ResearchGate social network is much higher than that of the academia. The relationship between the number of records, citations, H-index and co-authorship in Scopus with the metrics of citation number, citations, index, readers, RJ score and followers in ResearchGate is positive and significant. However, there is no significant relationship between Scopus scientometrics and the criteria of followers, viewers, and co-authors in the academia.

Network theory techniques have recently contributed to the analysis of electrical power systems, enabling faster computational solutions. Taking advantage of the topological information of a network, it becomes
possible to characterize its elements both locally (individual network components) and globally (interactions and behavior of the components). Identifying the crucial elements within an electrical system involves
classifying each component based on its interaction with the entire network, considering, possibly, various operating conditions. Current network centrality measures predominantly focus on nodes, which represent connection buses in the system, to quantify the significance of individual elements. In this study, we employ the linegraph technique to transform links into nodes. Subsequently, we calculate and categorize the links (representing lines and transformers) of different electrical networks found in the literature using three centrality measures. Moreover, our
methodology allows for the aggregation or combination of the indices from each measure, leading to a unified classification based on the importance of links in the considered electrical power systems. Analyzing diverse networks reveals a consistent empirical distribution of centrality indices, resulting in similar classifications of significant elements regardless of network size.

Viral marketing campaigns target primarily those individuals who are central in social networks and hence have social influence. Marketing events, however, may attract diverse audience. Despite the importance of event marketing, the influence of heterogeneous target groups is not well understood yet. In this paper, we define the Spreading Potential (SP) problem in which different sets of agents need to evaluated and compared based on their social influence. A typical application of SP is choosing locations for a series of marketing events. The SP problem is different from the well-known Influence Maximization (IM) problem in two aspects. Firstly, it deals with sets rather than nodes. Secondly, the sets are diverse, composed by a mixture of influential and ordinary agents. Thus, SP needs to assess the contribution of ordinary agents too, while IM only aims to find top spreaders. We provide a systemic test for ranking influence measures in the SP problem based on node sampling and on a novel statistical method, the Sum of Ranking Differences. Using a Linear Threshold diffusion model on an online social network, we evaluate seven network 1

Graph Neural Networks (GNNs) extend basic Neural Networks (NNs) by using graph structures based on the relational inductive bias (homophily assumption). While GNNs have been commonly believed to outperform NNs in real-world tasks, recent work has identified a non-trivial set of datasets where their performance compared to NNs is not satisfactory. Heterophily has been considered the main cause of this empirical observation and numerous works have been put forward to address it. In this paper, we first revisit the widely used homophily metrics and point out that their consideration of only graph-label consistency is a shortcoming. Then, we study heterophily from the perspective of post-aggregation node similarity and define new homophily metrics, which are potentially advantageous compared to existing ones. Based on this investigation, we prove that some harmful cases of heterophily can be effectively addressed by local diversification operation. Then, we propose the Adaptive Channel Mixing (ACM), a framework to adaptively exploit aggregation, diversification and identity channels node-wisely to extract richer localized information for diverse node heterophily situations. ACM is more powerful than the commonly used uni-channel framework for node classification tasks on heterophilic graphs and is easy to be implemented in baseline GNN layers. When evaluated on 10 benchmark node classification tasks, ACM-augmented baselines consistently achieve significant performance gain, exceeding state-of-theart GNNs on most tasks without incurring significant computational burden.

Taking into account that accessibility is one of the most strategic and determining factors in economic models and that accessibility and tourism affect each other, we can say that the study and improvement of one of them involved the development of the other. Using network analysis, this study presents an algorithm for labeling the difficulty of the streets of a city using different accessibility parameters. We combine network structure and accessibility factors to explore the association between innovative behavior within the street network, and the relationships with the commercial activity in a city. Finally, we present a case study of the city of Avila, locating the most inaccessible areas of the city using centrality measures and analyzing the effects, in terms of accessibility, on the commerce and services of the city.

In recent years there has been a growing interest in simulating competitive markets to find out the efficient ways to advertise a product or spread an ideology. Along this line, we consider a binary competitive contagion process where two infections, A and B, interact with each other and diffuse simultaneously in a network. We investigate which is the best centrality measure to find out the seed nodes a company should adopt in the presence of rivals so that it can maximize its influence. These nodes can be used as the initial spreaders or advertisers by firms when two firms compete with each other. Each node is assigned a price tag to become an initial advertiser which varies according to their importance in the network. Considering their fixed budgets, they initially determine the payoff of their products and the number of their initial seeds in the network. Under this setting, we study the question of whether to choose a small number of influential nodes or a larger number of less influential nodes.

Due to the importance of the interdisciplinary investigations in create of knowledge, this research study relationships between centrality metrics with researcher's scientific productivity and Performance and visualization of co-authorship social network in distance education. Methods: The present study is an applied study of scientometrics. The statistical population is the scientific productions (In overall 40252) of all researchers, which at least one of the articles is indexed in the Web of Science citations (ISI) database from 1992 to 2012. After preparation the co-authorship matrix of countries (C1) and researchers (AU), in order to extract the results, three types of softwares it has been used: (a) Social Network Analysis Softwares (UCINET & Bibexcel), (b) Visualization of Co-Authorship Social Network Softwares (Pajek & NetDraw) and (c) Statistical Analysis Softwares (SPSS). Findings: The results show that there is a growing growth in increase of co-authorship between scholars in distance education. Among the scholars, Liu, J; Chen, Y; Dodson, SC; Chen, X and Chen, J respectively have the highest measure of articles and also Chen, Y; Dodson, SC; Liu, B; Zhou, DX and Liu, J have the highest amount of citations received to the articles. Also in terms of the superior couples of the author, couples of (Liu J** Chen H) with 28 cases scientific collaboration had the highest rating and then couples of the (Chen Y ** chang C) and (Li Z ** Chen J) are in the next ranks. In addition, USA, Algeria, Argentina and Austria are ranked first to forth in terms of the number of records. In degree centrality, scholars such as Liu, J; Chen, Y and Dodson, SC, in closeness centrality, Chen, T; Liu, B and Chen, H and in betweenness centrality, Chen, H; Zhu, Y and Chen, J ranked first to third. Finally, the research findings showed that there is a significant relationship between the researcher's centrality scores with their scientific productivity and performance. The results indicate that the number of citations received by researchers is a function of the number of articles published by them. Also, researchers in a co-authorship social network have social influence that have earned a higher centrality score.

In this paper, we present some results about the spectrum of the matrix associated with the computation of the Multiplex PageRank defined by the authors in a previous paper. These results can be considered as a natural extension of the known results about the spectrum of the Google matrix. In particular, we show that the eigenvalues of the transition matrix associated with the multiplex network can be deduced from the eigenvalues of a block matrix containing the stochastic matrices defined for each layer. We also show that, as occurs in the classic PageRank, the spectrum is not affected by the personalization vectors defined on each layer but depends on the parameter α that controls the teleportation. We also give some analytical relations between the eigenvalues and we include some small examples illustrating the main results.

PageRank can be understood as the stationary distribution of a Markov chain that occurs in a two-layer network with the same set of nodes in both layers: the physical layer and the teleportation layer. In this paper we present some bounds for the extension of this two-layer approach to Multiplex networks, establishing sharp estimates for this Multiplex PageRank and locating the possible values of the personalized PageRank for each node of a network. Several examples are shown to compare the values obtained for both algorithms, the classic and the two-layer PageRank.

The availability of the resources in communication networks is critical, due to the impact that possible disruptions of communication services may have in the society. Therefore providing adequate levels of availability for every demand in a network is of paramount importance. In this work, we focus on the topological structure of a network to select a set of links that provide a high availability path to be used by the different end-to-end demands. This set of links constitutes a high availability structure (the spine) and is used as the working path for each demand. The backup path for each demand is edge-disjoint with the corresponding working path. This path pair provides end-to-end protection for critical service demands in the network. An exact formulation of the problem is presented and solved for small instances networks. A heuristic resolution approach with centrality measures is also put forward, with an experimental study comparing the exact and the approximate results.

The determination of node centrality is a fundamental topic in social network studies. In contrast to established metrics, which identify central nodes based on their brokerage power, the number and weight of their connections, and the ability to quickly reach all other nodes, we introduce five new measures of Distinctiveness Centrality. Those new metrics attribute a larger value to keeping a connection with the network periphery instead. We compute their main features, i.e. range and expected value for the class of scale-free networks. The results show that they are all consistent with the goal of keeping the network periphery connected, and provide a viewpoint of centrality alternative to that of established metrics.

Objective: The purpose of this research was studying the future of the dissemination of scientific productions of Knowledge and Information Science in social networks. Methodology: This research was carried out using an applied method employing a mixed method approach containing scientometric methods, content analysis, Delphi technique, scenario writing and survey methods to conduct futures studies on the dissemination of scientific production of information science and library researchers in social networks. To conduct futures studies, we need to understand the current needs and interests of researchers in each field of science,that all articles of Knowledge and Information Science indexed in the Web of Science from 2005 to mid-2016 has been investigated in terms of altmetric indicators and subject areas were identified by quantitative content analysis method in terms of dissemination. Then, in the future studies section, Delphi technique, survey methods, and scenario writing ‫اطالع‬ ‫و‬ ‫کتابداری‬ ‫رسانی‬ ، ‫دوره‬ 22 ، ‫شماره‬ 3 ، ‫پیاپی‬ ‫شماره‬ 87 ، ‫پاییز‬ 8338 837 approach were used to predict the status of dissemination of scientific productions in future years in social networks. Findings: According to the study, social networks such as ResearchGate, Mendeley, and Academia will be more appreciated by researchers in the field of Knowledge and Information Science. It was also found that the subject areas such as library and information science, computational studies, information retrieval, are among the top priorities for research in the social networks in the next ten years. The compound annual growth rate of the dissemination of scientific production of information science and library researchers in social networks was found to be 14.5% and the growth of the dissemination of scientific productions of Knowledge and Information Science researchers is expected to follow the continuation scenario. According to the views of Iranian researchers who are active in social networks, the qualitative development of scientific production, the attractiveness of research topics and self-archiving are expected to influence the dissemination rate in the coming years more than other factors. Conclusion: The results showed that social networks continuously play the role of disseminators of scientific information and are not limited in disseminating information in the same way as some traditional platforms are. In effect, it is possible to use the dissemination rate as a complementary measure to other altmetric indicators in assessing researchers' productions in social networks. Dissemination score can be used as one of the complementary measures of Altmetrics indicators in projection trends, future predictions and evaluation of researchers in social networks, the dissemination of information on social networks are more than other factors would be related to the quality of scientific output. Researchers in the field of Knowledge and Information Science can use the results of this research to improve future planning.

Scientific collaboration has always been of interest to researchers. The analyses of data relating to scientific collaboration is one of the techniques by which we can evaluate research activities. Co-authorship network analysis can represent good information regarding the patterns and structures of co-authorship. Social network analysis was used as the research method. The research population included twenty journals of Information Science which had an impact factor of 0.635 as a minimum from the years 1996 to 2010. The research findings showed that Journal of the American Medical Informatics Association with 0/3 network density has a highest co-authorship network density. Low connection existed in coauthorship network of Information Science journals and co-authorship networks of these journals were loose and sparse. The Results showed that co-authorship networks of information science journals had a low density. Compactness of this journal is low and co-authorship networks had a low cohesion. Results of this research also showed that the density of co-authorship networks of Information Science is lower than Medical Sciences and higher than Management and Social Computations.

Background and aim: Altmetrics seeks to assess the scientific impact with new ways using data derived from the social Web. The aim of this paper aims to represent the concept, benefits, disadvantages and challenges of Altmetrics. Material and methods: This review article was conducted using the related literature. Findings: Unlike to the traditional evaluation methods which are done based on three filters &#39;peer review&#39;, &#39;number of citations&#39;, and &#39;impact factors&#39;, are time-consuming and can not to assess all the scientific productions, altmetrics evaluates the scientific productions, researchers&#39; popularity and scientific cooperation in web and social networks using faster, broader, and more different metrics. However, altmetrics encounters to criticism and challenges such as the changing nature of web, lack of theory, and ease of scientific trick. Conclusion: Impact is a multi-dimensional concept and traditional citation methods cannot measure all aspect...

Ce travail propose une modélisation adéquate en graphes pour les systèmes et séquences accidentelles de sûreté nucléaire. Ces systèmes et séquences proviennent des "Etudes Probabilistes de Sûreté" (EPS) qui consistent à analyser de façon exhaustive tous les scénarios accidentels envisageables, d'estimer leurs probabilités d'occurrence (en les regroupant par famille) et les conséquences associées. Ensuite une analyse des réseaux complexes résultants est effectuée par des mesures de centralités. Une première application consiste à la prédiction du Facteur d'Accroissement du Risque nucléaire en utilisant les algorithmes d'apprentissages supervisé : méthodes à base d'arbre de classification, régression logistique et méthodes ensemblistes, sur des données déséquilibrées. Par ailleurs, un nouveau coefficient synthétique de centralité et une mesure de similarité sont conçus pour comparer les structures de réseaux, indépendamment de leurs caractéristiques topologiques, en se basant sur les interdépendances entre leurs vecteurs de centralités. Cette nouvelle approche utilise des techniques statistiques (échantillonnage, corrélation et homogénéité). La pertinence et l'efficacité de cette nouvelle mesure de similarité sont validées sur le clustering de graphes théoriques classiques et la prédiction du type de graphes. Enfin, une application de cette approche est réalisée pour le clustering des réseaux complexes des systèmes de sûreté nucléaire.

Ce travail propose une modélisation adéquate en graphes pour les systèmes et séquences accidentelles de sûreté nucléaire. Ces systèmes et séquences proviennent des "Etudes Probabilistes de Sûreté" (EPS) qui consistent à analyser de façon exhaustive tous les scénarios accidentels envisageables, d'estimer leurs probabilités d'occurrence (en les regroupant par famille) et les conséquences associées. Ensuite une analyse des réseaux complexes résultants est effectuée par des mesures de centralités. Une première application consiste à la prédiction du Facteur d'Accroissement du Risque nucléaire en utilisant les algorithmes d'apprentissages supervisé : méthodes à base d'arbre de classification, régression logistique et méthodes ensemblistes, sur des données déséquilibrées. Par ailleurs, un nouveau coefficient synthétique de centralité et une mesure de similarité sont conçus pour comparer les structures de réseaux, indépendamment de leurs caractéristiques topologiques, en se basant sur les interdépendances entre leurs vecteurs de centralités. Cette nouvelle approche utilise des techniques statistiques (échantillonnage, corrélation et homogénéité). La pertinence et l'efficacité de cette nouvelle mesure de similarité sont validées sur le clustering de graphes théoriques classiques et la prédiction du type de graphes. Enfin, une application de cette approche est réalisée pour le clustering des réseaux complexes des systèmes de sûreté nucléaire.

Online social networks play an important role as a suitable platform for information diffusion. While positive news diffusion on social network has a great impact in people's life, the negative news can also spread as fast as positive ones. To make the social network a reliable place, it is necessary to block inappropriate, unwanted and contamination diffusion. In this paper, we study the notion of competing negative and positive campaigns in a social network and address the influence blocking maximization (IBM) problem to minimize the bad effect of misinformation. IBM problem can be summarized as identifying a subset of nodes to adopt the positive influence under Multicampaign Independent Cascade Model (MCICM) as diffusion model to minimize the number of nodes that adopt the negative influence at the end of both propagation processes. We proposed Centrality_IBM algorithm based on centrality measures for finding an appropriate candidate subset of nodes for spreading positive diffusion in order to minimizing the IBM problem. Then, we experimentally compare the performance of the proposed algorithm using some centrality measures to choose the appropriate subset of positive influential nodes. The experiments on different real datasets reveal that the closeness centrality measure outperforms the alternative centrality measures in most of the cases.

Introduction: With the significant expansion of research, we are witnessing the discrediting of some scientific outputs in the field of medicine. This study endeavored to investigate the dimensions and patterns of ooperation of internationally discredited works in the field of medicine in the Scopus database.
Methods: This study is applied in terms of purpose and in terms of onducting research and data analysis, it is quantitative and has been done using bibliometric analysis method and scientometric pproach and llustration techniques to draw scientific collaborations. The population is all the discredited medical works available from 2016 to the end of 2020 in the Scopus database which has been done using the network analysis method.
Results: The findings showed that during the period, 480 works published in Scopus database were discredited. The Unites States, England, India, and China have the highest index of centrality, intimacy, and rosscontextuality. These countries play an important role in connecting nodes and transmitting information over the network.
Conclusion: Discredited articles in the United States and England have igh centrality indices, which indicates the greater influence and power of hese countries, which, in turn, have a greater influence on other countries in the scientific network.
Keywords: Scientometrics; Retracted Publication; Database; Scientific ollaborations; Journal Article

We study the causal impact of network centrality on educational outcomes using field experiments in primary schools in Bangladesh. After obtaining information on friendship networks, we randomly allocate students into groups and give them individual and group assignments. We find that groups that perform best are those whose members have high Katz-Bonacich and key-player centralities. Leaders are mostly responsible for this effect, while bad apples have little influence. Own Katz-Bonacich centrality is associated with better individual performance only if it is above the average centrality of the group. Further experiments reveal that leadership, as measured by network centrality, mainly captures non-cognitive skills, especially patience and competitiveness.

In this study, we constructed the data table of acupoint functions (i.e., acupoint indications and clinical applications) based on the previously developed information system of acupoint diagnosis and treatment in Traditional Chinese Medicine. Based on the data table of acupoint functions, between-acupoint point correlations were calculated. Acupoints with statistically significant point correlations were linked to construct the acupoint network with functional similarity. The degree centrality values of acupoints (totally 311 acupoints) showed that the acupoints Zhengying (GB17), Qinglengyuan (SJ11), Jiaji (EX-B2), etc. have the highest degree centrality values. Most of these acupoints are located on the head and neck, and their functions are universal. The acupoints Yinbai (SP1) and Zhongkui (EX-UE4) have strong specific functions and weak substitutability. The results of frequency distribution, skewness, aggregation index, coefficient of variation, entropy, and probability distributions showed that the obtained acupoint network is a scale-free complex network. Among them, the probability density function of the power law distribution is p(x)=x-6.1818 , x≥36.

http://www.iaees.org/publications/journals/nb/articles/2023-13(3)/1-Zhang-Abstract.asp

Network Biology (ISSN 2220-8879; CODEN NBEICS)

Volume 13, Number 3, 1 September 2023
http://www.iaees.org/publications/journals/nb/articles/2023-13(3)/2023-13(3).asp

Articles

Construction and analysis of acupoint network with functional similarity in Traditional Chinese Medicine
Network Biology, 2023, 13(3): 74-83
WenJun Zhang, YanHong Qi
[Abstract] [XML] [EndNote] [RefManager] [BibTex] [DOAJ] [PubMed]
[ Full PDF (278K)][Supplementary Material (449K)][Chinese Version (411K)][Animated Interactive Network]
[Email Article] [Comment/Review Article]

Graphical representation of genetic code algebra
Network Biology, 2023, 13(3): 84-97
Birinchi Kumar Boruah, Tazid Ali
[Abstract] [XML] [EndNote] [RefManager] [BibTex] [DOAJ] [PubMed]
[ Full PDF (744K)]
[Email Article] [Comment/Review Article]

Community detection in network is of vital importance to find cohesive subgroups. Node attributes can improve the accuracy of community detection when combined with link information in a graph. Community detection using node attributes has not been investigated in detail. To explore the aforementioned idea, we have adopted an approach by modifying the Louvain algorithm. We have proposed Louvain-AND-Attribute (LAA) and Louvain-OR-Attribute (LOA) methods to analyze the effect of using node attributes with modularity. We compared this approach with existing community detection approaches using different datasets. We found the performance of both algorithms better than Newman's Eigenvector method in achieving modularity and relatively good results of gain in modularity in LAA than LOA. We used density, internal and external edge density for the evaluation of quality of detected communities. LOA provided highly dense partitions in the network as compared to Louvain and Eigenvector algorithms and close values to Clauset. Moreover, LOA achieved few numbers of edges between communities.

The availability of the resources in communication networks is critical, due to the impact that possible disruptions of communication services may have in the society. Therefore providing adequate levels of availability for every demand in a network is of paramount importance. In this work, we focus on the topological structure of a network to select a set of links that provide a high availability path to be used by the different end-to-end demands. This set of links constitutes a high availability structure (the spine) and is used as the working path for each demand. The backup path for each demand is edge-disjoint with the corresponding working path. This path pair provides end-to-end protection for critical service demands in the network. An exact formulation of the problem is presented and solved for small instances networks. A heuristic resolution approach with centrality measures is also put forward, with an experimental study comparing the exact and the approximate results.

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Background and Objectives: Most of the budget and revenues of each country are spent on research and development processes in order to achieve scientific progress. But the success of each country in achieving this goal is not simply measurable. Evaluation of scientific achievements is based on two main pillars of quantity and quality. The purpose of this study is to investigate the status of citation competition of Iranian researchers' articles in national journals and identify Iranian core journals in the three groups of citation core journals, publishing core journals and Matthew core journals.
Methodology: The present study was a citation analysis one. The sample was consists of scientific articles of the top five universities in Iran. The sample size includes 49328 articles that have been published in 6658 journals. Since the data of this research is taken from Scopus citation database, instead of using the impact factor index, the "journal cite score" is used to show the journal citation impact. The cite score of each journal shows the average number of citations per article over a three-year period for each journal, so it can be used as the expected value for all articles in that journal. For this purpose, in this study, to calculate the number of citations expected for each journal. In this study, core journals were divided into three groups. The first group is Publishing Core Magazines (PCJ), the second group is Citation Core Magazines (CCJ) and the third group is Matthew Core Magazines (MCJ); These are journals that contain half of Iran's articles, journals that contain half of the citations received by Iran, and journals that contain half of Matthew's citations (either positive or negative) in Iran.
Findings: Researchers in the study sample have published in a total of 6658 journals, which includes a total of 49328 articles. With the condition of publishing at least ten articles from Iran in the five years under review for each journal, 994 journals remained as a collection of national journals in Iran. The number of journals in the collection of national journals of Iran (994 journal titles) is only 15% of the total journals (6658 journal titles) that Iranian researchers have selected to publish the article during the five years of study. It is noteworthy that this small percentage of journals, more than half of the articles (55.64%) and up to 70% of the total citations. This information indicates the importance of these journals and the concentration of a large number of articles and citations in a small group of journals. Among the core journals, Matthew Negative Nuclear Magazines is the largest group, accounting for 193 journals and nearly 20% of the total INJS journals. After that, the group of publishing core journals (182 journals) and citation core journals (107 journals) had the largest number of journals, respectively. Matthew Core Negative Magazines, on the other hand, have the lowest number of citations in the period under review, despite having the highest number of journals. This indicates that there are a large number of journals in the collection of national journals of Iran that have not had a proper visibility for Iranian articles. But the positive group of Matthew Core Magazines, which is the smallest group of Core Magazines, despite the very small number of magazines (only 14 titles), but accounted for approximately 11% of the total citations. The main feature of these magazines is that they have been able to occupy half of the citations of Matthew in Iranian magazines.
Discussion: A review of the collections of core journals showed that more than half of the journals do not belong to any of the core groups. On the other hand, in this study, it was found that Matthew core positive journals, the journals that contain half of the citation performance of Iranian articles, are only 14 titles. Perhaps by adopting better publishing strategies and offering advice to Iranian scientists, the number of these journals can be increased. Recently, Iran has always had brilliant rankings in number of articles, so that sometimes it has even surpassed the global growth rate. However, a review of the core journals shows that these journals have not performed well in obtaining citations and credibility, and a large group of them are in the group of negative Matthew core journals (49 titles). This shows that the increase in quantity and number of articles does not necessarily lead to an increase in citation and scientific credibility. Therefore, it is better to choose solutions to increase the visibility of scientific works so that in parallel with increasing the number of articles, appropriate recognition can be received. In general, it seems that the adoption of appropriate research and publishing strategies, as well as the selection of a strong and credible journal, is necessary to improve the citation performance of Iranian articles in the field of scientific competition. Obviously, this does not happen overnight and requires the design and implementation of appropriate short-term and long-term scientific development programs. Ideally, a country magazine collection should be the most reputable collection. However, for countries with poor scientific infrastructure, this may in itself be detrimental; because the acceptance process and, consequently, the quantity of their products affects. Therefore, such systems can, as a suitable alternative, seek to find a set with more visible chances (Sotoudeh, 2011).

In this paper, we present some results about the spectrum of the matrix associated with the computation of the Multiplex PageRank defined by the authors in a previous paper. These results can be considered as a natural extension of the known results about the spectrum of the Google matrix. In particular, we show that the eigenvalues of the transition matrix associated with the multiplex network can be deduced from the eigenvalues of a block matrix containing the stochastic matrices defined for each layer. We also show that, as occurs in the classic PageRank, the spectrum is not affected by the personalization vectors defined on each layer but depends on the parameter α that controls the teleportation. We also give some analytical relations between the eigenvalues and we include some small examples illustrating the main results.