Centrality Measure

The growth in size and complexity of supply chains has led to compounded risk exposure, which is hard to measure with existing risk management approaches. In this study, we apply the concept of systemic risk to show that centrality metrics can be used for complex supply network risk assessment. We review and select metrics, and set up an exemplary case applied to the material flow and contractual networks of Honda Acura. In the exemplary case study, geographical risk information is incorporated to selected systemic risk assessment metrics and results are compared to assessment without risk indicators in order to draw conclusions on how additional information can enhance systemic risk assessment in supply networks. Katz centrality is used to measure the node's risk spread using the World Risk Index. Authority and hub centralities are applied to measure the link risk spread using distances between geographical locations. Closeness is used to measure speed of disruption spread. Betweenness centrality is used to identify high risk middlemen. Our results indicate that these metrics are successful in identifying vulnerabilities in network structure even in simplified cases, which risk practitioners can use to extend with historical data to gain more accurate insights into systemic risk exposure.

We live in a world of social networks. Our everyday choices are often influenced by social interactions. Word of mouth, meme di↵usion on the Internet, and viral marketing are all examples of how social networks can a↵ect our behaviour. In many practical applications, it is of great interest to determine which nodes have the highest influence over the network, i.e., which set of nodes will, indirectly, reach the largest audience when propagating information. These nodes might be, for instance, the target for early adopters of a product, the most influential endorsers in political elections, or the most important investors in financial operations, just to name a few examples. Here, we tackle the NP-hard problem of influence maximization on social networks by means of a Genetic Algorithm. We show that, by using simple genetic operators, it is possible to find in feasible runtime solutions of high-influence that are comparable, and occasionally better, than the solutions found by a number of known heuristics (one of which was previously proven to have the best possible approximation guarantee, in polynomial time, of the optimal solution). The advantages of Genetic Algorithms show, however, in them not requiring any assumptions about the graph underlying the network, and in them obtaining more diverse sets of feasible solutions than current heuristics.

During the translation process, the genetic code is the nucleotide sequence that determines the amino acid sequence of protein molecules. A codon is a universal triplet of nucleotides that codes for an amino acid. A group G's identity graph is a graph in which the vertex set is the set of all group elements and two vertices in G are adjacent if a.b = e, where e is the group's identity element. In this study, we looked at the identity graph in the genetic code algebra. In our current study, we have thoroughly discussed various measures of centrality. In addition to this analysis, the correlation coefficients between various centrality measures, clustering coefficient, degree of distribution, and skewness are all examined.

http://www.iaees.org/publications/journals/nb/articles/2023-13(3)/2-Boruah-Abstract.asp

Only when understanding hackers' tactics, can we thwart their attacks. With this spirit, this paper studies how hackers can effectively launch the so-called 'targeted node attacks', in which iterative attacks are staged on a network, and in each iteration the most important node is removed. In the existing attacks for weighted networks, the node importance is typically measured by the centralities related to shortest-path lengths, and the attack effectiveness is also measured mostly by length-related metrics. However, this paper argues that flows can better reflect network functioning than shortest-path lengths for those networks with carrying traffic as the main functionality. Thus, this paper proposes metrics based on flows for measuring the node importance and the attack effectiveness, respectively. Our node importance metrics include three flow-based centralities (flow betweenness, current-flow betweenness and current-flow closeness), which have not been proposed for use in the attacks on weighted networks yet. Our attack effectiveness metric is a new one proposed by us based on average network flow. Extensive experiments on both artificial and real-world networks show that the attack methods with our three suggested centralities are more effective than the existing attack methods when evaluated under our proposed attack effectiveness metric.

The paper addresses the problem of finding top k influential nodes in large scale directed social networks. We propose two new centrality measures, Diffusion Degree for independent cascade model of information diffusion and Maximum Influence Degree. Unlike other existing centrality measures, diffusion degree considers neighbors' contributions in addition to the degree of a node. The measure also works flawlessly with non uniform propagation probability distributions. On the other hand, Maximum Influence Degree provides the maximum theoretically possible influence (Upper Bound) for a node. Extensive experiments are performed with five different real life large scale directed social networks. With independent cascade model, we perform experiments for both uniform and non uniform propagation probabilities. We use Diffusion Degree Heuristic (DiDH) and Maximum Influence Degree Heuristic (MIDH), to find the top k influential individuals. k seeds obtained through these for both the setups show superior influence compared to the seeds obtained by high degree heuristics, degree discount heuristics, different variants of set covering greedy algorithms and Prefix excluding Maximum Influence Arborescence (PMIA) algorithm. The superiority of the proposed method is also found to be statistically significant as per T-test.

The problem of target set selection for large scale social networks is addressed in the paper. We describe a novel deprecation based greedy strategy to be applied over a pre-ordered (as obtained with any heuristic influence function) set of nodes. The proposed algorithm runs in iteration and has two stages, (i) Estimation: where the performance of each node is evaluated and (ii) Marking: where the nodes to be deprecated in later iterations are marked. We have theoretically proved that for any monotonic and sub-modular influence function, the algorithm correctly identifies the nodes to be deprecated. For any finite set of input nodes it is shown that the algorithm can meet the ending criteria. The worst case performance of the algorithm, both in terms of time and performance, is also analyzed. Experimental results on seven un-weighted as well as weighted social networks show that the proposed strategy improves the ranking of the input seeds in terms of the total number of nodes influenced.

Epidemic modeling in complex networks has become one of the latest topics in recent times. The Susceptible-Infectious-Recovered (SIR) model and its variants are often used for epidemic modeling. One important issue in epidemic modeling is the determination of the spreading ability of the nodes in the network. Thus, for example, can be detected in the early stages. In this study, we developed a centrality measure called Lexical Sorting Centrality (LSC) that distinguishes the spreading ability of the nodes. Using other centrality measures calculated for the nodes, LSC sorts the nodes in a way similar to alphabetical order. We conducted simulations on six datasets using SIR to evaluate the performance of LSC and compared LSC with degree centrality (DC), eigenvector centrality (EC), closeness centrality (CC), betweenness centrality (BC) and Gravitational Centrality (GC). Experimental results show that LSC distinguishes the spreading ability of the nodes more accurately, more decisively, and faster.

Given a budget and arbitrary cost for selecting each node, the budgeted influence maximization (BIM) problem concerns selecting a set of seed nodes to disseminate some information that maximizes the total number of nodes influenced (termed as influence spread) in social networks at a total cost no more than the budget. Our proposed seed selection algorithm for the BIM problem guarantees an approximation ratio of (1 − 1/ √ e). The seed selection algorithm needs to calculate the influence spread of candidate seed sets, which is known to be #P-complex. Identifying the linkage between the computation of marginal probabilities in Bayesian networks and the influence spread, we devise efficient heuristic algorithms for the latter problem. Experiments using both large-scale social networks and synthetically generated networks demonstrate superior performance of the proposed algorithm with moderate computation costs. Moreover, synthetic datasets allow us to vary the network parameters and gain important insights on the impact of graph structures on the performance of different algorithms.

Influence maximization is introduced to maximize the profit of viral marketing in social networks. The weakness of influence maximization is that it does not distinguish specific users from others, even if some items can be only useful for the specific users. For such items, it is a better strategy to focus on maximizing the influence on the specific users. In this paper, we formulate an influence maximization problem as query processing to distinguish specific users from others. We show that the query processing problem is NP-hard and its objective function is submodular. We propose an expectation model for the value of the objective function and a fast greedy-based approximation method using the expectation model. For the expectation model, we investigate a relationship of paths between users. For the greedy method, we work out an efficient incremental updating of the marginal gain to our objective function. We conduct experiments to evaluate the proposed method with real-life datasets, and compare the results with those of existing methods that are adapted to the problem. From our experimental results, the proposed method is at least an order of magnitude faster than the existing methods in most cases while achieving high accuracy.

The evolution and spread of social networks have attracted the interest of the scientific community in the last few years. Specifically, several new interesting problems, which are hard to solve, have arisen in the context of viral marketing, disease analysis, and influence analysis, among others. Companies and researchers try to find the elements that maximize profit, stop pandemics, etc. This family of problems is collected under the term Social Network Influence Maximization problem (SNIMP), whose goal is to find the most influential users (commonly known as seeds) in a social network, simulating an influence diffusion model. SNIMP is known to be an $$\mathcal {NP}$$ NP -hard problem and, therefore, an exact algorithm is not suitable for solving it optimally in reasonable computing time. The main drawback of this optimization problem lies on the computational effort required to evaluate a solution. Since each node is infected with a certain probability, the objective function val...

Network Biology (ISSN 2220-8879; CODEN NBEICS)

Volume 9, Number 3, 1 September 2019 

Cover Pages
[Front Pages (114K)] [Back Pages (77K)]

Articles

Average reachability: A new metric to estimate epidemic growth considering the network structure and epidemic severity
Network Biology, 2019, 9(3): 42-57
Bita Shams, Mohammad Khansari
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Stability, bifurcation and chaos control in a discrete-time prey-predator model with Holling type-II response
Network Biology, 2019, 9(3): 58-77
Muhammad Salman Khan, Muhammad Asif Khan, Muhammad Sajjad Shabbir, Qamar Din
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[ Full PDF (426K)]
[Email Article] [Comment/Review Article]

Influence maximization problem is one of the challenges in online social networks. This problem refers to finding a small set of members of a social network, by activation of which information propagation can be maximized using one of the propagation models such as independent cascade model. For the maximization problem, the greedy algorithm has been presented which is close to optimal response by 67% in terms of accuracy; but, the problem of this method is its inefficiency in the social networks with a large number of members. The performed works on the improvement of the greedy algorithm have been mostly faced with the problem of scalability, dependence on graph structure, or need for large memory. In this paper, a method was presented using automata learning which could preserve its efficiency in large social networks and obtainresults with near-optimal values. For this purpose, space of the problem was reduced by removing low-degree nodes and the effective nodes for starting propagation in social network was found by automata learning which is optimal for achieving global optimization. The obtained results of this paper showed that the proposed method was efficient in large social networks and its results were close to the ones obtained by the greedy algorithm in terms of accuracy.

Effective immunization of individual communities with minimal cost in vaccination has made great discussion surrounding the realm of complex networks. Meanwhile, proper realization of relationship among people in society and applying it to social networks brings about substantial improvements in immunization. Accordingly, weighted graph in which link weights represent the intensity and intimacy of relationships is an acceptable approach. In this work we employ weighted graphs and a wide variety of weighted centrality measures to distinguish important individuals in contagion of diseases. Furthermore, we propose new centrality measures for weighted networks. Our experimental results show that Radiality-Degree centrality is satisfying for weighted BA networks. Additionally, PageRank-Degree and Radiality-Degree centralities showmoreacceptable performance in targeted immunization of weighted networks.

The paper addresses the problem of finding top k influential nodes in large scale directed social networks. We propose two new centrality measures, Diffusion Degree for independent
cascade model of information diffusion and Maximum Influence Degree. Unlike other existing centrality measures, diffusion degree considers neighbors’ contributions in addition to the degree of a node. The measure also works flawlessly with non uniform propagation probability distributions. On the other hand, Maximum Influence Degree provides the maximum theoretically possible influence (Upper Bound) for a node. Extensive experiments are performed with five different real life
large scale directed social networks. With independent cascade model, we perform experiments for both uniform and non uniform propagation probabilities. We use Diffusion Degree Heuristic (DiDH) and Maximum Influence Degree Heuristic (MIDH), to find the top k influential individuals. k seeds
obtained through these for both the setups show superior influence compared to the seeds obtained by high degree heuristics, degree discount heuristics, different variants of set covering greedy algorithms and Prefix excluding Maximum Influence Arborescence (PMIA) algorithm. The superiority
of the proposed method is also found to be statistically significant as per T-test.

Abstract Network-analysis literature is rich in node-centrality measures that quantify the centrality of a node as a function of the (shortest) paths of the network that go through it. Existing work focuses on defining instances of such measures and designing algorithms for the specific combinatorial problems that arise for each instance. In this work, we propose a unifying definition of centrality that subsumes all path-counting based centrality definitions: eg, stress, betweenness or paths centrality.