Geometric properties of graph layouts optimized for greedy navigation

The graph layouts used for complex network studies have been mainly developed to improve visualization. If we interpret the layouts in metric spaces such as Euclidean ones, however, the embedded spatial information can be a valuable cue for various purposes. In this work, we focus on encoding useful navigational information to geometric coordinates of vertices of spatial graphs, which is a reverse problem of harnessing geometric information for better navigation. In other words, the coordinates of the vertices are a map of the topology, not the other way around. We use a recently developed user-centric navigation protocol to explore spatial layouts of complex networks that are optimal for navigation. These layouts are generated with a simple simulated annealing optimization technique. We compare these layouts to others targeted at better visualization and discuss the spatial statistical properties of the optimized layouts for better navigability and its implication.

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

[2]  Marián Boguñá,et al.  Navigability of Complex Networks , 2007, ArXiv.

[3]  E. Aurell,et al.  Behavior of heuristics on large and hard satisfiability problems. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Satoru Kawai,et al.  An Algorithm for Drawing General Undirected Graphs , 1989, Inf. Process. Lett..

[5]  Marc Barthelemy,et al.  Spatial Networks , 2010, Encyclopedia of Social Network Analysis and Mining.

[6]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[7]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[8]  B. Hillier,et al.  The Social Logic of Space , 1984 .

[9]  D. Vernon.  Inform , 1995, Encyclopedia of the UN Sustainable Development Goals.

[10]  Remo Guidieri.  Res , 1995, RES: Anthropology and Aesthetics.

[11]  Sang Hoon Lee,et al.  Pathlength scaling in graphs with incomplete navigational information , 2011, ArXiv.

[12]  Marián Boguñá,et al.  Navigating ultrasmall worlds in ultrashort time. , 2008, Physical review letters.

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

[14]  Sang Hoon Lee,et al.  Exploring maps with greedy navigators , 2011, Physical review letters.

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

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

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

[18]  Michael T. Gastner,et al.  Price of anarchy in transportation networks: efficiency and optimality control. , 2007, Physical review letters.

[19]  K Sneppen,et al.  Networks and cities: an information perspective. , 2005, Physical review letters.

[20]  Sang Hoon Lee,et al.  A greedy-navigator approach to navigable city plans , 2012, ArXiv.

[21]  Laura A. Carlson,et al.  Getting Lost in Buildings , 2010 .

[22]  S. N. Dorogovtsev,et al.  Evolution of networks , 2001, cond-mat/0106144.

[23]  W. Zachary,et al.  An Information Flow Model for Conflict and Fission in Small Groups , 1977, Journal of Anthropological Research.

[24]  Beom Jun Kim,et al.  Growing scale-free networks with tunable clustering. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.