Semirings for temporal network analysis

Springer eBooks, 2017

A set with one or more operations defined on it and rules that hold for them Network analysis: A study of networks as representations of relations between discrete objects Sparse matrix: A matrix with most of entries equal to zero Large network: A network with several thousands or millions of nodes Complete graph: K n-A graph in which every pair of nodes is linked Definition A network can be represented also with a corresponding matrix. Using matrix operations (addition and multiplication) over an appropriate semiring a unified approach to several network analysis problems can be developed. Matrix multiplication is about traveling on network.

Journal of Mathematical Sociology, 1994

In the paper four semirings for solving social networks problems are constructed. The closures of the matrix of a given signed graph over balance and cluster semirings can be used to decide whether the graph is balanced or clusterable.

Journal of The ACM, 2010

Betweenness centrality measure is often used in social and computer communication networks to estimate the potential monitoring and control capabilities a vertex may have on data flowing in the network. In this paper we define the Routing Betweenness Centrality (RBC) measure which generalizes previously well known Betweenness measures such as the Shortest Path Betweenness, Flow Betweenness, and Traffic Load Centrality by considering network flows created by arbitrary loop-free routing strategies.

2021

This report documents the program and the outcomes of Dagstuhl Seminar 121171 "Temporal Graphs: Structure, Algorithms, Applications". The seminar was organized around four core areas: models, concepts, classes; concrete algorithmic problems; distributed aspects; applications. Because of the ongoing pandemic crisis, the seminar had to be held fully online, with talk and open problems sessions focussing on afternoons. Besides 19 contributed talks and small-group discussions, there were lively open-problem sessions, and some of the problems and research directions proposed there are part of this document. Despite strongly missing the usual Dagstuhl atmosphere and personal interaction possibilities, the seminar helped to establish new contacts and to identify new research directions in a thriving research area between (algorithmic) graph theory and network science.

Many networks are dynamic in that their topology changes rapidly-on the same time scale as the communications of interest between network nodes. Examples are the human contact networks involved in the transmission of disease, ad hoc radio networks between moving vehicles, and the transactions between principals in a market. While we have good models of static networks, so far these have been lacking for the dynamic case. In this paper we present a simple but powerful model, the time-ordered graph, which reduces a dynamic network to a static network with directed flows. This enables us to extend network properties such as vertex degree, closeness, and betweenness centrality metrics in a very natural way to the dynamic case. We then demonstrate how our model applies to a number of interesting edge cases, such as where the network connectivity depends on a small number of highly mobile vertices or edges, and show that our centrality definition allows us to track the evolution of connectivity. Finally we apply our model and techniques to two real-world dynamic graphs of human contact networks and then discuss the implication of temporal centrality metrics in the real world.

2012

Records of time-stamped social interactions between pairs of individuals (e.g., face-to-face conversations, e-mail exchanges, and phone calls) constitute a so-called temporal network. A remarkable difference between temporal networks and conventional static networks is that time-stamped events rather than links are the unit elements generating the collective behavior of nodes. We propose an importance measure for single interaction events. By generalizing the concept of the advance of event proposed by [Kossinets G, Kleinberg J and Watts D J 2008 Proceeding of the 14th ACM SIGKDD International conference on knowledge discovery and data mining p 435], we propose that an event is central when it carries new information about others to the two nodes involved in the event. We find that the proposed measure properly quantifies the importance of events in connecting nodes along time-ordered paths. Because of strong heterogeneity in the importance of events present in real data, a small fr...

Delay-tolerant networks (DTNs) are characterized by a possible absence of end-to-end communication routes at any instant. In most cases, however, a form of connectivity can be established over time and space. This particularity leads to consider the relevance of a given route not only in terms of hops (topological length), but also in terms of time (temporal length). The problem of measuring temporal distances between individuals in a social network was recently addressed, based on a posteriori analysis of interaction traces. This paper focuses on the distributed version of this problem, asking whether every node in a network can know precisely and in real time how out-ofdate it is with respect to every other. Answering affirmatively is simple when contacts between the nodes are punctual, using the temporal adaptation of vector clocks provided in . It becomes more difficult when contacts have a duration and can overlap in time with each other. We demonstrate that the problem remains solvable with arbitrarily long contacts and non-instantaneous (though invariant and known) propagation delays on edges. This is done constructively by extending the temporal adaptation of vector clocks to non-punctual causality. The second part of the paper discusses how the knowledge of temporal lags could be used as a building block to solve more concrete problems, such as the construction of foremost broadcast trees or network backbones in periodically-varying DTNs.

International Journal of Computer Applications, 2012

As communication is important, it is not the entire thing rather something more interesting as well as complicated. Closely related is how processes cooperate and synchronize with one another. In a distributed system an application may have several processes that run concurrently on multiple nodes of the system. For correct results, several such distributed applications require that the clocks of the nodes are synchronized with each other. For concurrency we have used vector clock method .But there are several disadvantages. For that we have developed a new algorithm for vector clock method from which we can define the concurrency among processes. In our proposed algorithm the vector of each process's local clock consists of (n+1) parameter where n is the number of processes in the system. The (n+1) th parameter is used as a flag which help to discuss the concurrency among different processes..

Physical Review E, 2019

Network properties govern the rate and extent of various spreading processes, from simple contagions to complex cascades. Recently, the analysis of spreading processes has been extended from static networks to temporal networks, where nodes and links appear and disappear. We focus on the effects of "accessibility", whether there is a temporally consistent path from one node to another, and "reachability", the density of the corresponding "accessibility graph" representation of the temporal network. The level of reachability thus inherently limits the possible extent of any spreading process on the temporal network. We study reachability in terms of the overall levels of temporal concurrency between edges and the structural cohesion of the network agglomerating over all edges. We use simulation results and develop heterogeneous mean field model predictions for random networks to better quantify how the properties of the underlying temporal network regulate reachability.

media.mit.edu

Network planning and traffic flow optimization requires the acquirement and analysis of large quantities of data such as the network topology, its traffic flow data, vehicle fleet composition, emission measurements etc. Data acquirement is an expensive process that involves household surveys and automatic as well as semi-automatic measurements performed all over the network. For example, in order to accurately estimate the effect of a certain network change on the total emissions produced by vehicles in the network, assessment of the vehicle fleet composition for each origin-destination pair is required. As a result, problems that optimize non-local merit functions becomes highly difficult to solve. One such problem is finding the optimal deployment of traffic monitoring units. In this paper we suggest a new traffic assignment model that is based on the concept of Shortest Path Betweenness Centrality measure borrowed from the domain of complex network analysis. We show how Betweenness can be augmented in order to solve the traffic assignment problem given an arbitrary travel cost definition. The proposed traffic assignment model is evaluated using a high resolution Israeli transportation dataset derived from the analysis of cellular phones data. The group variant of the augmented Betweenness Centrality is then used to optimize the locations of traffic monitoring units, hence reducing the cost and increasing the effectiveness of traffic monitoring. ⋆