Complex networks on hyperbolic surfaces

被引：93
作者：
Aste, T [1 ]
Di Matteo, T [1 ]
Hyde, ST [1 ]
机构：
[1] Australian Natl Univ, Res Sch Phys Sci, Canberra, ACT 0200, Australia
来源：
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2005年 / 346卷 / 1-2期
关键词：
networks; complex systems; hyperbolic graphs; econophysics;
D O I：
10.1016/j.physa.2004.08.045
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We explore a novel method to generate and characterize complex networks by means of their embedding on hyperbolic surfaces. Evolution through local elementary moves allows the exploration of the ensemble of networks which share common embeddings and consequently share similar hierarchical properties. This method provides a new perspective to classify network-complexity both on local and global scale. We demonstrate by means of. several examples that there is a strong relation between the network properties and the embedding surface. (C) 2004 Elsevier B.V. All rights reserved.
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收藏
页码：20 / 26
页数：7
相关论文
共 30 条
[11]   PLANAR DIAGRAMS [J].
BREZIN, E ;
ITZYKSON, C ;
PARISI, G ;
ZUBER, JB .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1978, 59 (01) :35-51
[12]   Scale-free networks are ultrasmall [J].
Cohen, R ;
Havlin, S .
PHYSICAL REVIEW LETTERS, 2003, 90 (05) :4
[13]  
Coxeter H. S. M., 1973, REGULAR POLYTOPES
[14]  
DIMATTEO T, 2004, PREPRINT
[15]   Two-dimensional froths and the dynamics of biological tissues [J].
Dubertret, B ;
Aste, T ;
Ohlenbusch, HM ;
Rivier, N .
PHYSICAL REVIEW E, 1998, 58 (05) :6368-6378
[16]  
ERDOS P, 1960, B INT STATIST INST, V38, P343
[17]  
GILBIN PJ, 1981, GRAPHS SURFACES HOMO
[18]   TOPOLOGICAL CORRELATIONS IN CELLULAR STRUCTURES AND PLANAR GRAPH-THEORY [J].
GODRECHE, C ;
KOSTOV, I ;
YEKUTIELI, I .
PHYSICAL REVIEW LETTERS, 1992, 69 (18) :2674-2677
[19]   Ab-initio construction of some crystalline 3D Euclidean networks [J].
Hyde, ST ;
Ramsden, S ;
Di Matteo, T ;
Longdell, JJ .
SOLID STATE SCIENCES, 2003, 5 (01) :35-45
[20]   Some novel three-dimensional Euclidean crystalline networks derived from two-dimensional hyperbolic tilings [J].
Hyde, ST ;
Ramsden, S .
EUROPEAN PHYSICAL JOURNAL B, 2003, 31 (02) :273-284
123