Resistance and Security Index of Networks: Structural Information Perspective of Network Security

Recently, Li and Pan defined the metric of the K-dimensional structure entropy of a structured noisy dataset G to be the information that controls the formation of the K-dimensional structure of G that is evolved by the rules, order and laws of G, excluding the random variations that occur in G. Here, we propose the notion of resistance of networks based on the one- and two-dimensional structural information of graphs. Given a graph G, we define the resistance of G, written , as the greatest overall number of bits required to determine the code of the module that is accessible via random walks with stationary distribution in G, from which the random walks cannot escape. We show that the resistance of networks follows the resistance law of networks, that is, for a network G, the resistance of G is , where and are the one- and two-dimensional structure entropies of G, respectively. Based on the resistance law, we define the security index of a network G to be the normalised resistance of G, that is, . We show that the resistance and security index are both well-defined measures for the security of the networks.

[1]  Wei Zhang,et al.  Strategies for network security , 2014, Science China Information Sciences.

[2]  D S Callaway,et al.  Network robustness and fragility: percolation on random graphs. , 2000, Physical review letters.

[3]  Cohen,et al.  Resilience of the internet to random breakdowns , 2000, Physical review letters.

[4]  C. Causer.  The Art of War , 2011, IEEE Potentials.

[5]  Hans J. Herrmann,et al.  Mitigation of malicious attacks on networks , 2011, Proceedings of the National Academy of Sciences.

[6]  Paulo Shakarian,et al.  Finding Near-Optimal Groups of Epidemic Spreaders in a Complex Network , 2014, PloS one.

[7]  P. Kaye.  Infectious diseases of humans: Dynamics and control , 1993 .

[8]  George Leitmann,et al.  Dynamics and Control , 2020, Fundamentals of Robotics.

[9]  Adilson E Motter.  Cascade control and defense in complex networks. , 2004, Physical review letters.

[10]  Alessandro Vespignani,et al.  Epidemic spreading in scale-free networks. , 2000, Physical review letters.

[11]  Éva Tardos,et al.  Maximizing the Spread of Influence through a Social Network , 2015, Theory Comput..

[12]  B. Bollobás.  The evolution of random graphs , 1984 .

[13]  Albert-László Barabási,et al.  Error and attack tolerance of complex networks , 2000, Nature.

[14]  Angsheng Li,et al.  Discovering natural communities in networks , 2015 .

[15]  Angsheng Li,et al.  Homophyly/Kinship Model: Naturally Evolving Networks , 2015, Scientific Reports.

[16]  Angsheng Li,et al.  A Theory of Network Security: Principles of Natural Selection and Combinatorics , 2016, Internet Math..

[17]  S. Havlin,et al.  Optimization of network robustness to waves of targeted and random attacks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Abhijit Sarkar,et al.  Two-peak and three-peak optimal complex networks. , 2004, Physical review letters.

[19]  Reuven Cohen,et al.  Efficient immunization strategies for computer networks and populations. , 2002, Physical review letters.

[20]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.

[21]  R. May,et al.  Infectious Diseases of Humans: Dynamics and Control , 1991, Annals of Internal Medicine.

[22]  M. Keeling,et al.  Networks and epidemic models , 2005, Journal of The Royal Society Interface.

[23]  Albert-László Barabási,et al.  Scale-Free Networks: A Decade and Beyond , 2009, Science.

[24]  Duncan J Watts,et al.  A simple model of global cascades on random networks , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[25]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[26]  Ken Sakamura,et al.  A New Challenge , 2001 .

[27]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[28]  Frederick P. Brooks,et al.  Three great challenges for half-century-old computer science , 2003, JACM.

[29]  Claude E. Shannon,et al.  The lattice theory of information , 1953, Trans. IRE Prof. Group Inf. Theory.

[30]  Joseph Christmas,et al.  The Decade and beyond , 1991 .

[31]  Angsheng Li,et al.  Three-Dimensional Gene Map of Cancer Cell Types: Structural Entropy Minimisation Principle for Defining Tumour Subtypes , 2016, Scientific Reports.

[32]  S. Havlin,et al.  Breakdown of the internet under intentional attack. , 2000, Physical review letters.

[33]  E. Young.  Contagion , 2015, New Scientist.