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  • Graph Theory
  • 1
    In: IEEE Transactions on Circuits and Systems I: Regular Papers, 04/2012, Vol.59(4), pp.763-771
    Description: A simple topology-manipulative algorithm for control of virus spreading trough complex networks is suggested. The algorithm is studied and applied on an SIS model type of an infection, and the system is described with a set of nonlinear difference probabilistic equations, that represent the dynamics of infection probabilities of nodes and existence probabilities of links in the graph. The validity of the control mechanism is first proven theoretically. Then, simulations are performed and results from both the realistic (status dependent) and probabilistic (analyzed) systems are compared, proving numerically as well, that the suggested algorithm is valid tool for infection eradication from complex networks. Several strategies of control implementation were tested and efficiency of each evaluated on the probabilistic system.
    Keywords: Components, Circuits, Devices and Systems;
    ISSN: 1549-8328
    E-ISSN: 1558-0806
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  • 2
    Language: English
    In: Physica A: Statistical Mechanics and its Applications, 2010, Vol.389(11), pp.2290-2299
    Description: Rich-club and page-club coefficients and their null models are introduced for directed graphs. Null models allow for a quantitative discussion of the rich-club and page-club phenomena. These coefficients are computed for four directed real-world networks: Arxiv High Energy Physics paper citation network, Web network (released from Google), Citation network among US Patents, and email network from a EU research institution. The results show a high correlation between rich-club and page-club ordering. For journal paper citation network, we identify both rich-club and page-club ordering, showing that “elite” papers are cited by other “elite” papers. Google web network shows partial rich-club and page-club ordering up to some point and then a narrow declining of the corresponding normalized coefficients, indicating the lack of rich-club ordering and the lack of page-club ordering, i.e. high in-degree (PageRank) pages purposely avoid sharing links with other high in-degree (PageRank) pages. For UC patents citation network, we identify page-club and rich-club ordering providing a conclusion that “elite” patents are cited by other “elite” patents. Finally, for email communication network we show lack of both rich-club and page-club ordering. We construct an example of synthetic network showing page-club ordering and the lack of rich-club ordering.
    Keywords: Directed Networks ; Rich-Club Coefficient ; Page-Club Coefficient ; Real Networks ; Physics
    ISSN: 0378-4371
    E-ISSN: 1873-2119
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  • 3
    Language: English
    In: Communications in Nonlinear Science and Numerical Simulation, 2011, Vol.16(1), pp.341-349
    Description: We consider normalized average edge betweenness of a network as a metric of network vulnerability. We suggest that normalized average edge betweenness together with is relative difference when certain number of nodes and/or edges are removed from the network is a measure of network vulnerability, called vulnerability index. Vulnerability index is calculated for four synthetic networks: Erdős–Rényi (ER) random networks, Barabási–Albert (BA) model of scale-free networks, Watts–Strogatz (WS) model of small-world networks, and geometric random networks. Real-world networks for which vulnerability index is calculated include: two human brain networks, three urban networks, one collaboration network, and two power grid networks. We find that WS model of small-world networks and biological networks (human brain networks) are the most robust networks among all networks studied in the paper.
    Keywords: Complex Networks ; Vulnerability ; Graph Theory ; Centrality Measures ; Network Topologies ; Applied Sciences
    ISSN: 1007-5704
    E-ISSN: 1878-7274
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  • 4
    Language: English
    In: Physica A: Statistical Mechanics and its Applications, 01 April 2017, Vol.471, pp.825-836
    Description: We show that three basic actor characteristics, namely normalized reciprocity, three cycles, and triplets, can be expressed using an unified framework that is based on computing the similarity index between two sets associated with the actor: the set of her/his friends and the set of those considering her/him as a friend. These metrics are extended to multiplex networks and then computed for two friendship networks generated by collecting data from two groups of undergraduate students. We found that in offline communication strong and weak ties are (almost) equally presented, while in online communication weak ties are dominant. Moreover, weak ties are much less reciprocal than strong ties. However, across different layers of the multiplex network reciprocities are preserved, while triads (measured with normalized three cycles and triplets) are not significant.
    Keywords: Multiplex Analysis ; Social Networks ; Graph Theory ; Physics
    ISSN: 0378-4371
    E-ISSN: 1873-2119
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