A Review of Recent Studies of Geographical Scale-Free Networks

The scale-free (SF) structures that commonly appear in many complex networks are a hot topic in social, biological, and information sciences. These self-organized generation mechanisms are expected to be useful for efficient communication or robust connectivity in socio-technological infrastructures. This paper is the first review of geographical SF network models. We discuss the essential generation mechanisms for inducing the structures with power-law behavior, and consider the properties of planarity and link length. Distributed design of geographical SF networks without the crossing and long-range links that cause interference and dissipation problems is very important for many applications such as communications, power grids, and sensor systems.

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

[2]  S. N. Dorogovtsev,et al.  Evolution of networks with aging of sites , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[3]  Lili Rong,et al.  High-dimensional random Apollonian networks , 2005, cond-mat/0502591.

[4]  I M Sokolov,et al.  Evolving networks with disadvantaged long-range connections. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Hans Mulder,et al.  Smart sensors to network the world. , 2004, Scientific American.

[6]  J. Jost,et al.  Evolving networks with distance preferences. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Tao Zhou,et al.  Maximal planar networks with large clustering coefficient and power-law degree distribution. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Albert-László Barabási,et al.  Error and attack tolerance of complex networks , 2000, Nature.

[9]  M. A. de Menezes,et al.  Shortest paths on systems with power-law distributed long-range connections. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  N. Konno,et al.  Geographical threshold graphs with small-world and scale-free properties. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Hiroyoshi Miwa,et al.  Analysis of scale-free networks based on a threshold graph with intrinsic vertex weights. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  BERNARD M. WAXMAN,et al.  Routing of multipoint connections , 1988, IEEE J. Sel. Areas Commun..

[13]  Reuven Cohen,et al.  Scale-free networks on lattices. , 2002, Physical review letters.

[14]  Keiko Imai,et al.  Structures of triangulations of points , 2000 .

[15]  Tao Zhou,et al.  Random Apollonian Networks , 2004 .

[16]  M. Newman,et al.  Mixing patterns in networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Tao Zhou,et al.  SIMPLEX TRIANGULATION INDUCED SCALE-FREE NETWORKS , 2005, cond-mat/0505175.

[18]  Jonathan P K Doye,et al.  Self-similar disk packings as model spatial scale-free networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  Xiaoyan Hong,et al.  Scalable routing protocols for mobile ad hoc networks , 2002, IEEE Netw..

[20]  Mark Buchanan,et al.  Nexus: Small Worlds and the Groundbreaking Science of Networks , 2002 .

[21]  Reka Albert,et al.  Mean-field theory for scale-free random networks , 1999 .

[22]  S. S. Manna,et al.  Growing spatial scale-free graphs by selecting local edges , 2005 .

[23]  L. Sander,et al.  Geography in a scale-free network model. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Edward Ott,et al.  Growing networks with geographical attachment preference: emergence of small worlds. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Marc Barthelemy.  Crossover from scale-free to spatial networks , 2002 .

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

[27]  Parongama Sen,et al.  Clustering properties of a generalized critical Euclidean network. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  R. Solé,et al.  Optimization in Complex Networks , 2001, cond-mat/0111222.

[29]  Hawoong Jeong,et al.  Modeling the Internet's large-scale topology , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[30]  J. S. Andrade,et al.  Apollonian networks: simultaneously scale-free, small world, euclidean, space filling, and with matching graphs. , 2004, Physical review letters.

[31]  Michael T. Gastner,et al.  The spatial structure of networks , 2006 .

[32]  M. A. Muñoz,et al.  Scale-free networks from varying vertex intrinsic fitness. , 2002, Physical review letters.

[33]  Reuven Cohen,et al.  Geographical embedding of scale-free networks , 2003 .

[34]  H E Stanley,et al.  Classes of small-world networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[35]  J. Doye.  Network topology of a potential energy landscape: a static scale-free network. , 2002, Physical review letters.

[36]  Parongama Sen,et al.  Modulated scale-free network in Euclidean space. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.