Modeling complex networks with self-similar outerplanar unclustered graphs

This paper introduces a family of modular, self-similar, small-world graphs with clustering zero. Relevant properties of this family are comparable to those of some networks associated with technological systems with a low clustering, like the power grid or some electronic circuits. Moreover, the graphs are outerplanar and it is know that many algorithms that are NP-complete for general graphs perform polynomial in outerplanar graphs. Therefore the graphs constitute a good mathematical model for these systems.

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

[2]  Reinhard Diestel,et al.  Graph Theory , 1997 .

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

[4]  M E J Newman.  Assortative mixing in networks. , 2002, Physical review letters.

[5]  Evelyn Fox Keller,et al.  Revisiting "scale-free" networks. , 2005, BioEssays : news and reviews in molecular, cellular and developmental biology.

[6]  André Raspaud,et al.  Recursive graphs with small-world scale-free properties. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Shlomo Havlin,et al.  Origins of fractality in the growth of complex networks , 2005, cond-mat/0507216.

[8]  Walter Willinger,et al.  Towards a Theory of Scale-Free Graphs: Definition, Properties, and Implications , 2005, Internet Math..

[9]  R. Solé,et al.  Information Theory of Complex Networks: On Evolution and Architectural Constraints , 2004 .

[10]  Lili Rong,et al.  Evolving small-world networks with geographical attachment preference , 2006 .

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

[12]  J. Guan,et al.  Maximal planar scale-free Sierpinski networks with small-world effect and power law strength-degree correlation , 2007, 0706.3490.

[13]  Shuigeng Zhou,et al.  A geometric growth model interpolating between regular and small-world networks , 2007, Journal of Physics A: Mathematical and Theoretical.

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

[15]  K. Goh,et al.  Fractality and self-similarity in scale-free networks , 2007 .

[16]  Shuigeng Zhou,et al.  From regular to growing small-world networks , 2006, cond-mat/0612624.

[17]  S. N. Dorogovtsev,et al.  Pseudofractal scale-free web. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  S. Havlin,et al.  Self-similarity of complex networks , 2005, Nature.

[19]  M. Weigt,et al.  On the properties of small-world network models , 1999, cond-mat/9903411.

[20]  R. F. Cancho,et al.  Topology of technology graphs: small world patterns in electronic circuits. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Jae Dong Noh,et al.  Exact scaling properties of a hierarchical network model. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Lali Barrière,et al.  The hierarchical product of graphs , 2009, Discret. Appl. Math..

[23]  Zhongzhi Zhang,et al.  Self-similar non-clustered planar graphs as models for complex networks , 2008, Journal of Physics A: Mathematical and Theoretical.

[24]  G. Fertin,et al.  High-dimensional Apollonian networks , 2005, cond-mat/0503316.

[25]  Chonghui Guo,et al.  A deterministic small-world network created by edge iterations , 2006 .

[26]  Albert-László Barabási,et al.  Hierarchical organization in complex networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  A. Brandstädt,et al.  Graph Classes: A Survey , 1987 .