On dynamic network security: A random decentering algorithm on graphs

M.T. Trobajo 1 , J. Cifuentes-Rodríguez 2  and M.V. Carriegos 1
  • 1 Departamento de Matemáticas, 24071, León, Spain
  • 2 Departamento de Tecnología Minera, Topográfica y de Estructuras, 24071, León, Spain


Random Decentering Algorithm (RDA) on a undirected unweighted graph is defined and tested over several concrete scale-free networks. RDA introduces ancillary nodes to the given network following basic principles of minimal cost, density preservation, centrality reduction and randomness. First simulations over scale-free networks show that RDA gives a significant decreasing of both betweenness centrality and closeness centrality and hence topological protection of network is improved. On the other hand, the procedure is performed without significant change of the density of connections of the given network. Thus ancillae are not distinguible from real nodes (in a straightforward way) and hence network is obfuscated to potential adversaries by our manipulation.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1]

    Brandes U., Erlebach T., Network Analysis, Lecture Notes in Computer Science, 1989, 3418, Springer.

  • [2]

    Borgatti S. P., Dynamic Social Network Modeling and Analysis, Workshop Summary and Papers, 2003.

  • [3]

    Borgatti S. P., Ajay M., Brass D. J., Labianca G., Network Analysis in the Social Sciences, Science, 2009, 892-895.

  • [4]

    Freeman L., The development of social network analysis, A Study in the Sociology of Science, 2004, 1.

  • [5]

    Seary A. J., Richards W. D., Dynamic Social Network Modeling and Analysis: Workshop Summary and Papers, Spectral methods for analyzing and visualizing networks: an introduction, 2003.

  • [6]

    Lozano M., García-Martínez C., Rodríguez F. J., Trujillo H. M., Optimizing network attacks by artificial bee colony, Information Sciences, 2017, 377, 30-50.

  • [7]

    Zhang B., Horvath S., A general framework for weighted gene coexpression network analysis, Statistical Applications in Genetics and Molecular Biology, 2005, 4.

  • [8]

    Guida M., Funaro M., Topology of the Italian airport network: A scale-free small-world network with a fractal structure?, Chaos, Solitons and Fractals, 2007, 31, 3, 527-536.

  • [9]

    Pedroche F., Romance M., Criado R., Some rankings based on PageRank applied to the Valencia metro, International Journal of Complex Systems in Science, 2016.

  • [10]

    Balci M. A., Fractional virus epidemic model on financial networks, Open Mathematics, 2016, 14, 1074-1086.

  • [11]

    Chapanond A., Krishnamoorthy M. S., Yener B., Graph theoretic and spectral analysis of Enron email data, Computational and Mathematical Organization Theory, 2005, 11, 265-281.

  • [12]

    Cvetović D., Simić S., Graph spectra in Computer Science, Linear Algebra and its Applications, 2011, 434, 6, 1545-1562.

  • [13]

    Dang-Pham D., Pittayachawan S., Bruno V., Applications of social network analysis in behavioural information security research: Concepts and empirical analysis, Computers & Security, 2017, 68, 1-15.

  • [14]

    Diestel R., Graph Theory. Graduate Texts in Mathematics, Springer-Verlag, 2005.

  • [15]

    Benito del Pozo P., Serrano N., Marqués-Sánchez P., Social networks and healthy cities: spreading good practices based on a spanish case study, Geographical Review, 2016.

  • [16]

    Pasqualetti F., Bicchi A., Bullo F., A graph-theoretical characterization of power network vulnerabilities, 2011, 3918-3923.

  • [17]

    Sridhar S., Hahn A., Govindarasu M., Cyber-Physical System Security for the Electric Power Grid, Proceedings of the IEEE, 2012, 100, 1, 210-224.

  • [18]

    Puzis R., Yagil D., Elovici Y., Braha D., Collaborative attack on Internet users’ anonymity, Internet Research, 2009, 19, 1, 60-77.

  • [19]

    Liu K., Das K., Grandison T., Kargupta H., Privacy-Preserving Data Analysis on Graphs and Social Networks, Next Generation of Data Minning, 2008.

  • [20]

    Arsič B., Cvetović D., Simić S., Škarić M., Graph spectral techniques in computer sciences, Applicable Analysis and Discrete Mathematics, 2012, 6, 1, 1-30.

  • [21]

    Cvetkoviı D., Rowlinson P., Simiı S., Eigenspaces of graphs, Eigenspaces of graphs, 1997, 66.

  • [22]

    Simic S. Andelic M., DaFonseca C. M., Zivkovic D., On the Multiplicities of Eigenvalues of Graphs and Their Vertex Deleted Subgraphs: Old and New Results, Electronic Journal of Linear Algebra, 2015, 30, 85-105 66.

  • [23]

    Shang, Y., Impact of self-healing capability on network robustness, Phys Rev E Stat Nonlin Soft Matter Phys., 2015, 91, 4, 042804.

  • [24]

    Shang, Y., Effect of link oriented self-healing on resilience of networks, Journal of Statistical Mechanics: Theory and Experiment, 2016, 8, 083403.

  • [25]

    Shang, Y., Localized recovery of complex networks against failure, Scient. Rep., 2016, 6, 30521 EP -.

  • [26]

    Holme P., Kim B. J., Yoon C., Han S. K., Attack vulnerability of complex networks, Phys. Rev. E, 2002, 65, 056109.

  • [27]

    Iyer S., Killingback T. and Sundaram B. Wang Z., Attack Robustness and Centrality of Complex Networks, PLoS ONE, 2013, 8, 4, e59613.

  • [28]

    Shang Y., Robustness of scale-free networks under attack with tunable grey information, EPL (Europhysics Letters), 2011, 95, 28005.

  • [29]

    West, D. B., Introduction to Graph Theory, Prentice Hall, 2001.

  • [30]

    Borgatti S. P., Everett M. G., A Graph-theoretic perspective on centrality, ESocial Networks, 2006, 28, 466-484.

  • [31]

    Bounova G. de Weck O., Overview of metrics and their correlation patterns for multiple-metric topology analysis on heterogeneous graph ensembles, Phys. Rev. E, 2012, 85, 016117.

  • [32]

    Canright G. S., Engø-Monsen K., Some Relevant Aspects of Network Analysis and Graph Theory, Elsevier, 2008, 361-424.

  • [33]

    Freeman L. C., Centrality in social networks conceptual clarification, Social Networks, 1978, 215-239.

  • [34]

    Latora V. Marchiori M., Efficient Behavior of Small-World Networks, Phys. Rev. Lett., 2001, 87, 19, 198701.

  • [35]

    LaVigne R. Zhang C. D. L., Maurer U. Moran T., Mularczyk M., Tschudi D., Topology-Hiding Computation Beyond Semi-Honest Adversaries, IACR Cryptology ePrint Archive, 2018, 255.

  • [36]

    Barabási A. L., Scale-Free Networks: A Decade and Beyond, Science, 2009, 325, 5939, 412-413.

  • [37]

    Barabási A. L., Réka A., Emergence of Scaling in Random Networks, Science, 1999, 286, 5439, 509-512.

  • [38]

    Barabási A. L., Réka A., Hawoong J., Mean-field theory for scale-free random networks, Physica A: Statistical Mechanics and its Applications, 1999, 272, 1-2, 173-187.

  • [39]

    Erdös P., Rényi A., On random graphs I, Publicationes Mathematicae (Debrecen), 1959, 6, 290-297.

  • [40]

    Meghanathan N., A Model for Generating Random Networks with Clustering Coefficient Corresponding to Real-World Network Graphs, International Journal of Control and Automation, 2016, 9, 163-176.

  • [41]

    Pedroche F., Criado R., Garcia E., Romance M., Matrix growth models based on centrality measures: a first analysis, International Journal of Complex Systems in Science, 2011, 1, 124-128.


Journal + Issues

Open Mathematics is a fully peer-reviewed, open access, electronic journal that publishes significant and original works in all areas of mathematics. The journal publishes both research papers and comprehensive and timely survey articles. Open Math aims at presenting high-impact and relevant research on topics across the full span of mathematics.