Identifying influential nodes in complex networks based on the inverse-square law

Abstract How to identify influential nodes in complex networks continues to be an open issue. A number of centrality measures have been presented to address this problem. However, these studies focus only on a centrality measure and each centrality measure has its own shortcomings and limitations. To solve problems above, in this paper, a novel method is proposed to identify influential nodes based on the inverse-square law. The mutual attraction between different nodes has been defined in complex network, which is inversely proportional to the square of the distance between two nodes. Then, the definition of intensity of node in a complex network is proposed and described as the sum of attraction between a pair of nodes in the network. The ranking method is presented based on the intensity of node, which can be considered as the influence of the node. In order to illustrate the effectiveness of the proposed method, several experiments are conducted to identify vital nodes simulations on four real networks, and the superiority of the proposed method can be demonstrated by the results of comparison experiments.

[1]  Guanrong Chen,et al.  Behaviors of susceptible-infected epidemics on scale-free networks with identical infectivity. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Meng Yang,et al.  A modified SIS model with an infective medium on complex networks and its global stability , 2011 .

[3]  Jürgen Kurths,et al.  Onymity promotes cooperation in social dilemma experiments , 2017, Science Advances.

[4]  Yong Deng,et al.  A New MADA Methodology Based on D Numbers , 2018, Int. J. Fuzzy Syst..

[5]  Duanbing Chen,et al.  Vital nodes identification in complex networks , 2016, ArXiv.

[6]  M. Kendall.  A NEW MEASURE OF RANK CORRELATION , 1938 .

[7]  Tao Zhou,et al.  Epidemic spreading on heterogeneous networks with identical infectivity , 2007 .

[8]  Yong Deng,et al.  A hybrid intelligent model for assessment of critical success factors in high-risk emergency system , 2018, Journal of Ambient Intelligence and Humanized Computing.

[9]  Fuyuan Xiao,et al.  An Improved Method for Combining Conflicting Evidences Based on the Similarity Measure and Belief Function Entropy , 2018, Int. J. Fuzzy Syst..

[10]  A Díaz-Guilera,et al.  Self-similar community structure in a network of human interactions. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Yicheng Zhang,et al.  Identifying influential nodes in complex networks , 2012 .

[12]  Yong Deng,et al.  Generating Z‐number based on OWA weights using maximum entropy , 2018, Int. J. Intell. Syst..

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

[14]  Hernán A. Makse,et al.  Influence maximization in complex networks through optimal percolation , 2015, Nature.

[15]  Xinyang Deng,et al.  An Evidential Axiomatic Design Approach for Decision Making Using the Evaluation of Belief Structure Satisfaction to Uncertain Target Values , 2018, Int. J. Intell. Syst..

[16]  Linyuan Lu,et al.  Link Prediction in Complex Networks: A Survey , 2010, ArXiv.

[17]  Yi-Cheng Zhang,et al.  Leaders in Social Networks, the Delicious Case , 2011, PloS one.

[18]  Duanbing Chen,et al.  Path diversity improves the identification of influential spreaders , 2013, ArXiv.

[19]  A. Barabasi,et al.  Network medicine : a network-based approach to human disease , 2010 .

[20]  Li Tao,et al.  New parallel processing strategies in complex event processing systems with data streams , 2017, Int. J. Distributed Sens. Networks.

[21]  Duanbing Chen,et al.  Identifying Influential Spreaders by Weighted LeaderRank , 2013, ArXiv.

[22]  Adilson E Motter,et al.  Cascade-based attacks on complex networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Xinyang Deng,et al.  D-AHP method with different credibility of information , 2017, Soft Computing.

[24]  Hernán A. Makse,et al.  Efficient collective influence maximization in cascading processes with first-order transitions , 2016, Scientific Reports.

[25]  Yong Deng,et al.  Measuring transferring similarity via local information , 2018 .

[26]  Zhen Wang,et al.  Spontaneous Symmetry Breaking in Interdependent Networked Game , 2014, Scientific Reports.

[27]  Phillip Bonacich,et al.  Eigenvector-like measures of centrality for asymmetric relations , 2001, Soc. Networks.

[28]  Tao Zhou,et al.  The H-index of a network node and its relation to degree and coreness , 2016, Nature Communications.

[29]  Yi Yu,et al.  System crash as dynamics of complex networks , 2016, Proceedings of the National Academy of Sciences.

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

[31]  Yong Deng,et al.  An enhanced fuzzy evidential DEMATEL method with its application to identify critical success factors , 2018, Soft Computing.

[32]  Lucas Antiqueira,et al.  Using metrics from complex networks to evaluate machine translation , 2011 .

[33]  Lin Wang,et al.  Coupled disease–behavior dynamics on complex networks: A review , 2015, Physics of Life Reviews.

[34]  Huijia Li,et al.  Punishment diminishes the benefits of network reciprocity in social dilemma experiments , 2017, Proceedings of the National Academy of Sciences.

[35]  Fuyuan Xiao,et al.  A Novel Evidence Theory and Fuzzy Preference Approach-Based Multi-Sensor Data Fusion Technique for Fault Diagnosis , 2017, Sensors.

[36]  Zhou Tao,et al.  Catastrophes in Scale-Free Networks , 2005 .

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

[38]  Yong Deng,et al.  Dependent Evidence Combination Based on Shearman Coefficient and Pearson Coefficient , 2018, IEEE Access.

[39]  Yong Deng,et al.  Evaluation method based on fuzzy relations between Dempster–Shafer belief structure , 2018, Int. J. Intell. Syst..

[40]  E. Schadt.  Molecular networks as sensors and drivers of common human diseases , 2009, Nature.

[41]  Rong Gao,et al.  FURTHER RESULTS OF CONVERGENCE OF UNCERTAIN RANDOM SEQUENCES , 2018 .

[42]  A. Díaz-Guilera,et al.  Efficiency of informational transfer in regular and complex networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[43]  Yong Deng,et al.  Toward uncertainty of weighted networks: An entropy-based model , 2018, Physica A: Statistical Mechanics and its Applications.

[44]  Bingyi Kang,et al.  Stable strategies analysis based on the utility of Z-number in the evolutionary games , 2018, Appl. Math. Comput..

[45]  Yong Deng,et al.  Generalized Ordered Propositions Fusion Based on Belief Entropy , 2018, Int. J. Comput. Commun. Control.

[46]  Qing Wang,et al.  Efficient processing of multiple nested event pattern queries over multi-dimensional event streams based on a triaxial hierarchical model , 2016, Artif. Intell. Medicine.

[47]  Hernán A. Makse,et al.  Collective Influence Algorithm to find influencers via optimal percolation in massively large social media , 2016, Scientific Reports.

[48]  Qiang Guo,et al.  Ranking the spreading influence in complex networks , 2013, ArXiv.

[49]  Hernán A. Makse,et al.  Collective Influence of Multiple Spreaders Evaluated by Tracing Real Information Flow in Large-Scale Social Networks , 2016, Scientific Reports.

[50]  Yong Deng,et al.  Failure mode and effects analysis based on D numbers and TOPSIS , 2016, Qual. Reliab. Eng. Int..

[51]  Flaviano Morone,et al.  Model of brain activation predicts the neural collective influence map of the brain , 2017, Proceedings of the National Academy of Sciences.

[52]  Liguo Fei,et al.  A new vector valued similarity measure for intuitionistic fuzzy sets based on OWA operators , 2019 .

[53]  János Kertész,et al.  Empirical study of the role of the topology in spreading on communication networks , 2016, ArXiv.

[54]  Dawei Zhao,et al.  Statistical physics of vaccination , 2016, ArXiv.

[55]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[56]  Yong Hu,et al.  A DEMATEL-based completion method for incomplete pairwise comparison matrix in AHP , 2016, Ann. Oper. Res..

[57]  Jürgen Kurths,et al.  Structural and functional clusters of complex brain networks , 2006 .

[58]  Lucas C. Parra,et al.  Collective Behaviour in Video Viewing: A Thermodynamic Analysis of Gaze Position , 2017, PloS one.

[59]  Wenxu Wang,et al.  Enhanced synchronizability by structural perturbations. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[60]  Tao Zhou,et al.  Immunization of susceptible–infected model on scale-free networks , 2006, physics/0610138.

[61]  Shlomo Havlin,et al.  Identifying influential directors in the United States corporate governance network. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[62]  Pablo M. Gleiser,et al.  Community Structure in Jazz , 2003, Adv. Complex Syst..

[63]  Wei Deng,et al.  Evidential Model Validation under Epistemic Uncertainty , 2018 .

[64]  John Skvoretz,et al.  Node centrality in weighted networks: Generalizing degree and shortest paths , 2010, Soc. Networks.

[65]  Ming Tang,et al.  Identify influential spreaders in complex networks, the role of neighborhood , 2015, ArXiv.

[66]  Yong Deng,et al.  A novel method for forecasting time series based on fuzzy logic and visibility graph , 2017, Advances in Data Analysis and Classification.

[67]  J. Faller,et al.  New Experimental Test of Coulomb's Law: A Laboratory Upper Limit on the Photon Rest Mass , 1971 .

[68]  V. Latora,et al.  A measure of centrality based on network efficiency , 2004, cond-mat/0402050.

[69]  A. Koyré.  An Unpublished Letter of Robert Hooke to Isaac Newton , 1952, Isis.

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

[71]  Yong Deng,et al.  Identifying influential nodes in complex networks: A node information dimension approach. , 2018, Chaos.

[72]  Xinyang Deng,et al.  Dependence assessment in human reliability analysis using an evidential network approach extended by belief rules and uncertainty measures , 2018, Annals of Nuclear Energy.

[73]  Jian-Fang Zhou,et al.  Spontaneous scale-free structure in adaptive networks with synchronously dynamical linking. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[74]  Qiang Guo,et al.  Locating influential nodes via dynamics-sensitive centrality , 2015, Scientific Reports.

[75]  Xinyang Deng,et al.  A Modified Method for Evaluating Sustainable Transport Solutions Based on AHP and Dempster–Shafer Evidence Theory , 2018 .