Scaling properties in time-varying networks with memory

Abstract The formation of network structure is mainly influenced by an individual node’s activity and its memory, where activity can usually be interpreted as the individual inherent property and memory can be represented by the interaction strength between nodes. In our study, we define the activity through the appearance pattern in the time-aggregated network representation, and quantify the memory through the contact pattern of empirical temporal networks. To address the role of activity and memory in epidemics on time-varying networks, we propose temporal-pattern coarsening of activity-driven growing networks with memory. In particular, we focus on the relation between time-scale coarsening and spreading dynamics in the context of dynamic scaling and finite-size scaling. Finally, we discuss the universality issue of spreading dynamics on time-varying networks for various memory-causality tests.

[1]  A. D. Medus,et al.  Memory effects induce structure in social networks with activity-driven agents , 2013, 1312.3496.

[2]  Piet Van Mieghem,et al.  Epidemic processes in complex networks , 2014, ArXiv.

[3]  Petter Holme,et al.  Modern temporal network theory: a colloquium , 2015, The European Physical Journal B.

[4]  Romualdo Pastor-Satorras,et al.  Burstiness and aging in social temporal networks , 2014, Physical review letters.

[5]  P. Holme.  Network reachability of real-world contact sequences. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Jari Saramäki,et al.  Exploring temporal networks with greedy walks , 2015, ArXiv.

[7]  Jari Saramäki,et al.  From calls to communities: a model for time-varying social networks , 2015, The European Physical Journal B.

[8]  S. N. Dorogovtsev,et al.  Structure of growing networks with preferential linking. , 2000, Physical review letters.

[9]  Ingo Scholtes,et al.  Causality-driven slow-down and speed-up of diffusion in non-Markovian temporal networks , 2013, Nature Communications.

[10]  Jari Saramäki,et al.  Temporal Networks , 2011, Encyclopedia of Social Network Analysis and Mining.

[11]  Naoki Masuda,et al.  Temporal networks: slowing down diffusion by long lasting interactions , 2013, Physical review letters.

[12]  V. Colizza,et al.  Analytical computation of the epidemic threshold on temporal networks , 2014, 1406.4815.

[13]  Petter Holme,et al.  Simulated Epidemics in an Empirical Spatiotemporal Network of 50,185 Sexual Contacts , 2010, PLoS Comput. Biol..

[14]  Alex Pentland,et al.  Reality mining: sensing complex social systems , 2006, Personal and Ubiquitous Computing.

[15]  Esteban Moro,et al.  Impact of human activity patterns on the dynamics of information diffusion. , 2009, Physical review letters.

[16]  Ciro Cattuto,et al.  Empirical temporal networks of face-to-face human interactions , 2013, The European Physical Journal Special Topics.

[17]  Kwang-Il Goh,et al.  Burstiness: Measures, Models, and Dynamic Consequences , 2013 .

[18]  Manfred Gilli,et al.  Understanding complex systems , 1981, Autom..

[19]  Ciro Cattuto,et al.  High-Resolution Measurements of Face-to-Face Contact Patterns in a Primary School , 2011, PloS one.

[20]  R. Pastor-Satorras,et al.  Activity driven modeling of time varying networks , 2012, Scientific Reports.

[21]  Ciro Cattuto,et al.  Dynamics of Person-to-Person Interactions from Distributed RFID Sensor Networks , 2010, PloS one.

[22]  PentlandAlex,et al.  Reality mining: sensing complex social systems , 2006 .

[23]  Jeremy Ginsberg,et al.  Detecting influenza epidemics using search engine query data , 2009, Nature.

[24]  Aravind Srinivasan,et al.  Modelling disease outbreaks in realistic urban social networks , 2004, Nature.

[25]  Igor M. Sokolov,et al.  Unfolding accessibility provides a macroscopic approach to temporal networks , 2012, Physical review letters.

[26]  Jari Saramäki,et al.  Temporal network sparsity and the slowing down of spreading , 2014, ArXiv.

[27]  Alain Barrat,et al.  How memory generates heterogeneous dynamics in temporal networks , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  Chaoming Song,et al.  Modelling the scaling properties of human mobility , 2010, 1010.0436.

[29]  S. Bornholdt,et al.  Scale-free topology of e-mail networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  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.

[31]  Romualdo Pastor-Satorras,et al.  Random walks on temporal networks. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[33]  Alessandro Vespignani,et al.  Time varying networks and the weakness of strong ties , 2013, Scientific Reports.

[34]  Rajmonda Sulo Caceres,et al.  Temporal Scale of Processes in Dynamic Networks , 2011, 2011 IEEE 11th International Conference on Data Mining Workshops.

[35]  Albert-László Barabási,et al.  Universal features of correlated bursty behaviour , 2011, Scientific Reports.

[36]  A. Vespignani.  Predicting the Behavior of Techno-Social Systems , 2009, Science.

[37]  M. Barthelemy,et al.  Microdynamics in stationary complex networks , 2008, Proceedings of the National Academy of Sciences.

[38]  A Barrat,et al.  Measuring contact patterns with wearable sensors: methods, data characteristics and applications to data-driven simulations of infectious diseases. , 2014, Clinical microbiology and infection : the official publication of the European Society of Clinical Microbiology and Infectious Diseases.

[39]  Carl T. Bergstrom,et al.  Mapping Change in Large Networks , 2008, PloS one.

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

[41]  Luis E C Rocha,et al.  Information dynamics shape the sexual networks of Internet-mediated prostitution , 2010, Proceedings of the National Academy of Sciences.