Paper Info
Title
On necessary conditions for scale-freedom in complex networks, with applications to computer communication systems
Abstract
Many complex networks exhibit a scale-free, power-law distribution of vertex degrees. This common feature is a consequence of two generic mechanisms relating to the formation of real networks: (i) networks tend to expand over time through the addition of new vertices and (ii) new vertices attach preferentially to those that are already well connected. We show that for many natural or man-made complex networks possessing a scale-free power-law distribution with the exponent γ ≥ 2, the number of degree-1 vertices, when nonzero, is of the same order as the network size N and that the average degree is of order at most log N. Our results expose another necessary characteristic of such networks. Furthermore, our method has the benefit of relying only on conditions that are static and easily verified for arbitrary networks. We use the preceding results to derive a closed-form formula approximating the distance distribution in scale-free networks. Such distributions are applied extensively in the fields of computer communication and software architecture, among other domains.
Year
DOI
Venue
2011
10.1080/00207720903267841
Int. J. Systems Science
Keywords
Field
DocType
scale free,complex system,complex network,scale free network,social network,small world network,graph,communication system,power law distribution,biological network,computer network
Discrete mathematics,Interdependent networks,Network motif,Spatial network,Small-world network,Evolving networks,Hierarchical network model,Degree distribution,Complex network,Mathematics
Journal
Volume
Issue
ISSN
42
6
0020-7721
Citations 
PageRank 
References 
5
0.57
11
Authors
3
Name
Order
Citations
PageRank
Wenjun Xiao121825.54
Weidong Chen2112.57
Behrooz Parhami3687104.30