Energy disruptive centrality with an application to criminal network

Abstract Many social interactions can be modeled by networks, where social actors are represented by vertices and their relations by edges. Researchers, over the years, have used social network analysis (SNA) to study the topological structure of the network and understand relational patterns. More recently, scholars have included in the SNA the actors’ attributes in the search for a better understanding, given that these attributes can influence the way that the relationships occur and consequently models the structure of the network. In this paper, we propose two centrality measures, based on the law of gravity, where the strength of the nodes’ attributes is combined with the strength of the relationships between them. We used an energy disruptive measure to target a network of convicts, monitored electronically, and the network of hijackers of Al Qaedas 9/11 attack with the aim of structurally and functionally dismantling it. The network damage was demonstrated by the robustness, measure which takes into account the size of the principal component, and also through two new measures proposed in this work: the attribute load, measure that analyzes the loss of nodes’ attributes; and the toughness, which takes into account the maximum sum of edges’ weights. Results show that, when used as a target method, the energy disruptive centrality was the most efficient strategy, providing greater network damage than other centrality measures analyzed.

[1]  Garry Robins,et al.  Understanding individual behaviors within covert networks: the interplay of individual qualities, psychological predispositions, and network effects , 2009 .

[2]  Ricardo Lopes de Andrade,et al.  P-means Centrality , 2019, Commun. Nonlinear Sci. Numer. Simul..

[3]  M. Newman,et al.  The structure of scientific collaboration networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

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

[5]  Anthony Dekker,et al.  Conceptual Distance in Social Network Analysis , 2005, J. Soc. Struct..

[6]  Herbert Hamers,et al.  Cooperative game theoretic centrality analysis of terrorist networks: The cases of Jemaah Islamiyah and Al Qaeda , 2013, Eur. J. Oper. Res..

[7]  Frank Schweitzer,et al.  A k-shell decomposition method for weighted networks , 2012, ArXiv.

[8]  P. Bonacich.  Factoring and weighting approaches to status scores and clique identification , 1972 .

[9]  C. Nick,et al.  Evaluation of anatomical and physiological traits of Solanum pennellii Cor. associated with plant yield in tomato plants under water-limited conditions , 2020, Scientific Reports.

[10]  Xiaoqi Ma,et al.  Identifying influential spreaders by gravity model , 2019, Scientific Reports.

[11]  Haifeng Yang,et al.  Logarithmic gravity centrality for identifying influential spreaders in dynamic large-scale social networks , 2017, 2017 IEEE International Conference on Communications (ICC).

[12]  Ernesto Estrada,et al.  Statistical-mechanical approach to subgraph centrality in complex networks , 2007, 0905.4098.

[13]  Guangyuan Fu,et al.  A new method to construct co-author networks , 2015 .

[14]  Sergey Brin,et al.  The Anatomy of a Large-Scale Hypertextual Web Search Engine , 1998, Comput. Networks.

[15]  Ricardo Lopes de Andrade,et al.  The use of nodes attributes in social network analysis with an application to an international trade network , 2018 .

[16]  Kathleen M. Carley,et al.  Destabilizing Dynamic Covert Networks , 2003 .

[17]  U. Brandes.  A faster algorithm for betweenness centrality , 2001 .

[18]  Xiang Yang Zhang,et al.  Effects of smoking on cognition and BDNF levels in a male Chinese population: relationship with BDNF Val66Met polymorphism , 2019, Scientific Reports.

[19]  Catherine S. Greenhill,et al.  The Use of Actor-Level Attributes and Centrality Measures to Identify Key Actors , 2015 .

[20]  James P. Gleeson,et al.  Assessing police topological efficiency in a major sting operation on the dark web , 2020, Scientific Reports.

[21]  Malcolm K. Sparrow,et al.  The application of network analysis to criminal intelligence: An assessment of the prospects , 1991 .

[22]  Gert Sabidussi,et al.  The centrality index of a graph , 1966 .

[23]  Eduardo L. Pasiliao,et al.  Finding clique clusters with the highest betweenness centrality , 2018, Eur. J. Oper. Res..

[24]  T. Killingback,et al.  Attack Robustness and Centrality of Complex Networks , 2013, PloS one.

[25]  Yannick Rochat,et al.  Closeness Centrality Extended to Unconnected Graphs: the Harmonic Centrality Index , 2009 .

[26]  Thomas Grund,et al.  Ethnic heterogeneity in the activity and structure of a Black street gang , 2012 .

[27]  Thomas Grund,et al.  Ethnic Homophily and Triad Closure , 2015 .

[28]  Igor Mishkovski,et al.  Vulnerability of complex networks , 2011 .

[29]  Phillip Bonacich,et al.  Some unique properties of eigenvector centrality , 2007, Soc. Networks.

[30]  Catherine S. Greenhill,et al.  Criminal network vulnerabilities and adaptations , 2017 .

[31]  Malcolm K. Sparrow,et al.  Network vulnerabilities and strategic intelligence in law enforcement , 1991 .

[32]  P. Duijn,et al.  The Relative Ineffectiveness of Criminal Network Disruption , 2014, Scientific Reports.

[33]  Cun-Quan Zhang,et al.  Terrorist Networks, Network Energy and Node Removal: A New Measure of Centrality Based on Laplacian Energy , 2013 .

[34]  Leonard M. Freeman,et al.  A set of measures of centrality based upon betweenness , 1977 .

[35]  M. Prokopenko,et al.  Percolation Centrality: Quantifying Graph-Theoretic Impact of Nodes during Percolation in Networks , 2013, PloS one.

[36]  P. Killworth,et al.  Informant accuracy in social network data III: A comparison of triadic structure in behavioral and cognitive data , 1979 .

[37]  Carlo Morselli,et al.  Assessing Vulnerable and Strategic Positions in a Criminal Network , 2010 .

[38]  John Lygeros,et al.  Optimal Sensor and Actuator Placement in Complex Dynamical Networks , 2013, ArXiv.

[39]  Valdis E. Krebs,et al.  Uncloaking Terrorist Networks , 2002, First Monday.

[40]  Scott G. McCalla,et al.  Crime Modeling with Lévy Flights , 2013, SIAM J. Appl. Math..

[41]  D. M. Schwartz,et al.  Using social network analysis to target criminal networks , 2009 .

[42]  Steven J. Strang.  Network Analysis in Criminal Intelligence , 2014 .

[43]  Balabhaskar Balasundaram,et al.  Detecting a most closeness-central clique in complex networks , 2020, Eur. J. Oper. Res..

[44]  Stephen P. Borgatti,et al.  Identifying sets of key players in a social network , 2006, Comput. Math. Organ. Theory.

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

[46]  Xin Chen,et al.  Analysis of complex network performance and heuristic node removal strategies , 2013, Commun. Nonlinear Sci. Numer. Simul..

[47]  Alessandro Vespignani,et al.  Vulnerability of weighted networks , 2006, physics/0603163.

[48]  Chuang Ma,et al.  Identifying influential spreaders in complex networks based on gravity formula , 2015, ArXiv.

[49]  Lev Muchnik,et al.  Identifying influential spreaders in complex networks , 2010, 1001.5285.

[50]  M. Newman.  Coauthorship networks and patterns of scientific collaboration , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[51]  L. Freeman.  Centrality in social networks conceptual clarification , 1978 .

[52]  Chao Li,et al.  Improved centrality indicators to characterize the nodal spreading capability in complex networks , 2018, Appl. Math. Comput..

[53]  P. Bonacich.  Power and Centrality: A Family of Measures , 1987, American Journal of Sociology.

[54]  T. Lumley,et al.  PRINCIPAL COMPONENT ANALYSIS AND FACTOR ANALYSIS , 2004, Statistical Methods for Biomedical Research.

[55]  P. Brantingham,et al.  Environment, Routine, and Situation: Toward a Pattern Theory of Crime (1993) , 2010 .