Unfolding accessibility provides a macroscopic approach to temporal networks

An accessibility graph of a network contains a link wherever there is a path of arbitrary length between two nodes. We generalize the concept of accessibility to temporal networks. Building an accessibility graph by consecutively adding paths of growing length (unfolding), we obtain information about the distribution of shortest path durations and characteristic time scales in temporal networks. Moreover, we define causal fidelity to measure the goodness of their static representation. The practicability of our proposed methods is demonstrated for three examples: networks of social contacts, livestock trade, and sexual contacts.

[1]  Víctor M Eguíluz,et al.  Coevolution of dynamical states and interactions in dynamic networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  A. Barrat,et al.  Dynamical Patterns of Cattle Trade Movements , 2011, PloS one.

[3]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

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

[5]  Stephen Warshall,et al.  A Theorem on Boolean Matrices , 1962, JACM.

[6]  Ciro Cattuto,et al.  What's in a crowd? Analysis of face-to-face behavioral networks , 2010, Journal of theoretical biology.

[7]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[8]  S. Wasserman,et al.  Social Network Analysis: Computer Programs , 1994 .

[9]  Thilo Gross,et al.  Adaptive coevolutionary networks: a review , 2007, Journal of The Royal Society Interface.

[10]  Maria A. Kazandjieva,et al.  A high-resolution human contact network for infectious disease transmission , 2010, Proceedings of the National Academy of Sciences.

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

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

[13]  Robin Wilson,et al.  Graphs and Applications_ An Introductory Approach , 2001 .

[14]  César A. Hidalgo,et al.  The Product Space Conditions the Development of Nations , 2007, Science.

[15]  A. Barrat,et al.  Simulation of an SEIR infectious disease model on the dynamic contact network of conference attendees , 2011, BMC medicine.

[16]  Matt J. Keeling,et al.  Networks and the Epidemiology of Infectious Disease , 2010, Interdisciplinary perspectives on infectious diseases.

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

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

[19]  Jari Saramäki,et al.  Path lengths, correlations, and centrality in temporal networks , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  L. Amaral,et al.  The web of human sexual contacts , 2001, Nature.

[21]  Matt J. Keeling,et al.  Representing the UK's cattle herd as static and dynamic networks , 2008, Proceedings of the Royal Society B: Biological Sciences.

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

[23]  T. Geisel,et al.  Forecast and control of epidemics in a globalized world. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[24]  Cecilia Mascolo,et al.  Components in time-varying graphs , 2011, Chaos.

[25]  M. Konschake,et al.  On the Robustness of In- and Out-Components in a Temporal Network , 2013, PloS one.

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

[27]  Robin Wilson,et al.  Graphs and Applications , 2000 .