symmetry in complex networks对称的复杂网络.pdf

Symmetry 2011, 3, 1-15; doi:10.3390/sym3010001 OPEN ACCESS symmetry ISSN 2073-8994 /journal/symmetry Article Symmetry in Complex Networks Angel Garrido Department of Fundamental Mathematics, Faculty of Sciences UNED, Senda del Rey 9, 28040 Madrid, Spain; E-Mail: agarrido@mat.uned.es (algbmv@) Received: 16 November 2010; in revised form: 4 January 2011 / Accepted: 7 January 2011 / Published: 10 January 2011 Abstract: In this paper, we analyze a few interrelated concepts about graphs, such as their degree, entropy, or their symmetry/asymmetry levels. These concepts prove useful in the study of different types of Systems, and particularly, in the analysis of Complex Networks. A System can be defined as any set of components functioning together as a whole. A systemic point of view allows us to isolate a part of the world, and so, we can focus on those aspects that interact more closely than others. Network Science analyzes the interconnections among diverse networks from different domains: physics, engineering, biology, semantics, and so on. Current developments in the quantitative analysis of Complex Networks, based on graph theory, have been rapidly translated to studies of brain network organization. The brains systems have complex network features—such as the small-world topology, highly connected hubs and modularity. These networks are not random. The topology of many different networks shows striking similarities, such as the scale-free structure