Emergence of Bursts and Communities in Evolving Weighted Networks

Understanding the patterns of human dynamics and social interaction and the way they lead to the formation of an organized and functional society are important issues especially for techno-social development. Addressing these issues of social networks has recently become possible through large scale data analysis of mobile phone call records, which has revealed the existence of modular or community structure with many links between nodes of the same community and relatively few links between nodes of different communities. The weights of links, e.g., the number of calls between two users, and the network topology are found correlated such that intra-community links are stronger compared to the weak inter-community links. This feature is known as Granovetter's “The strength of weak ties” hypothesis. In addition to this inhomogeneous community structure, the temporal patterns of human dynamics turn out to be inhomogeneous or bursty, characterized by the heavy tailed distribution of time interval between two consecutive events, i.e., inter-event time. In this paper, we study how the community structure and the bursty dynamics emerge together in a simple evolving weighted network model. The principal mechanisms behind these patterns are social interaction by cyclic closure, i.e., links to friends of friends and the focal closure, links to individuals sharing similar attributes or interests, and human dynamics by task handling process. These three mechanisms have been implemented as a network model with local attachment, global attachment, and priority-based queuing processes. By comprehensive numerical simulations we show that the interplay of these mechanisms leads to the emergence of heavy tailed inter-event time distribution and the evolution of Granovetter-type community structure. Moreover, the numerical results are found to be in qualitative agreement with empirical analysis results from mobile phone call dataset.

[1]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[2]  A-L Barabási,et al.  Structure and tie strengths in mobile communication networks , 2006, Proceedings of the National Academy of Sciences.

[3]  O. Bagasra,et al.  Proceedings of the National Academy of Sciences , 1914, Science.

[4]  J. Herskowitz,et al.  Proceedings of the National Academy of Sciences, USA , 1996, Current Biology.

[5]  October I.  Physical Review Letters , 2022 .

[6]  A. Vespignani,et al.  The architecture of complex weighted networks. , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[7]  Albert-László Barabási,et al.  The origin of bursts and heavy tails in human dynamics , 2005, Nature.

[8]  K. Goh,et al.  Spreading dynamics following bursty human activity patterns. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Gueorgi Kossinets,et al.  Empirical Analysis of an Evolving Social Network , 2006, Science.

[10]  Camille Roth,et al.  Connections: An Introduction to the Economics of Networks by Sanjeev Goyal , 2010, J. Artif. Soc. Soc. Simul..

[11]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[12]  M. Newman,et al.  Nonequilibrium phase transition in the coevolution of networks and opinions. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[14]  Juliana Freire,et al.  Proceedings of the 19th international conference on World wide web , 2010, WWW 2010.

[15]  B. Waclaw,et al.  Statistical mechanics of complex networks , 2007, 0704.3702.

[16]  Jari Saramäki,et al.  Emergence of communities in weighted networks. , 2007, Physical review letters.

[17]  L. Amaral,et al.  On Universality in Human Correspondence Activity , 2009, Science.

[18]  Won-kuk Cho,et al.  Generalized priority-queue network dynamics: impact of team and hierarchy. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  E. Kandel,et al.  Proceedings of the National Academy of Sciences of the United States of America. Annual subject and author indexes. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[20]  K-I Goh,et al.  Waiting time dynamics of priority-queue networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  S. Snyder,et al.  Proceedings of the National Academy of Sciences , 1999 .

[22]  Albert-László Barabási,et al.  Modeling bursts and heavy tails in human dynamics , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Alain Barrat,et al.  Social network dynamics of face-to-face interactions , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Albert-László Barabási,et al.  Understanding individual human mobility patterns , 2008, Nature.

[25]  S. Wasserman,et al.  Models and Methods in Social Network Analysis: Structural Analysis in the Social Sciences , 2005 .

[26]  A. Barabasi,et al.  Analysis of a large-scale weighted network of one-to-one human communication , 2007, physics/0702158.

[27]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[28]  Santo Fortunato,et al.  Community detection in graphs , 2009, ArXiv.

[29]  Jari Saramäki,et al.  Small But Slow World: How Network Topology and Burstiness Slow Down Spreading , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  Gerardo Iñiguez,et al.  Opinion and community formation in coevolving networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  Lauri Kovanen,et al.  Structure and dynamics of a large-scale complex social network , 2009 .

[32]  Andrew Gelman,et al.  Bursts: The Hidden Pattern Behind Everything We Do , 2010 .

[33]  Kathy P. Wheeler,et al.  Reviews of Modern Physics , 2013 .

[34]  Jean-Pierre Eckmann,et al.  Entropy of dialogues creates coherent structures in e-mail traffic. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[35]  A. Vazquez,et al.  Impact of interactions on human dynamics , 2007, 0710.4916.

[36]  Mark S. Granovetter.  The Strength of Weak Ties , 1973, American Journal of Sociology.

[37]  Hosung Park,et al.  What is Twitter, a social network or a news media? , 2010, WWW '10.

[38]  A. Barrat,et al.  Dynamical and bursty interactions in social networks. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  Jukka-Pekka Onnela,et al.  Spontaneous emergence of social influence in online systems , 2009, Proceedings of the National Academy of Sciences.

[40]  Mark Newman,et al.  Networks: An Introduction , 2010 .

[41]  Hawoong Jeong,et al.  Statistical properties of sampled networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[42]  Kimmo Kaski,et al.  Circadian pattern and burstiness in human communication activity , 2011, ArXiv.

[43]  Adilson E. Motter,et al.  A Poissonian explanation for heavy tails in e-mail communication , 2008, Proceedings of the National Academy of Sciences.

[44]  Jürgen Kurths,et al.  Evidence for a bimodal distribution in human communication , 2010, Proceedings of the National Academy of Sciences.