## Characterization of complex networks: A survey of measurements (2005)

Venue: | ADVANCES IN PHYSICS |

Citations: | 91 - 7 self |

### BibTeX

@INPROCEEDINGS{Costa05characterizationof,

author = {L. da F. Costa and F. A. Rodrigues and G. Travieso and P. R. Villas Boas},

title = {Characterization of complex networks: A survey of measurements},

booktitle = {ADVANCES IN PHYSICS},

year = {2005},

publisher = {}

}

### Years of Citing Articles

### OpenURL

### Abstract

Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics and function of processes executed on the network. The analysis, discrimination, and synthesis of complex networks therefore rely on the use of measurements capable of expressing the most relevant topological features. This article presents a survey of such measurements. It includes general considerations about complex network characterization, a brief review of the principal models, and the presentation of the main existing measurements organized into classes. Special attention is given to relating complex network analysis with the areas of pattern recognition and feature selection, as well as on surveying some concepts and measurements from traditional graph theory which are potentially useful for complex network research. Depending on the network and the analysis task one has in mind, a specific set of features may be chosen. It is hoped that the present survey will help the

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219 |
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Citation Context ...tics. A measure with better statistics is to computing the mean degree of the neighbors of nodes with a given degree [30], given by r = knn(k) = ∑ k ′ k ′ P(k ′ |k). (23) A related scalar measurement =-=[31]-=- is the Pearson correlation coefficient of the degrees at both ends of the links: ∑ 1 n i→j kikj [ ∑ 1 − n i→j 1 2 (ki ] 2 + kj) 1 n ∑ i→j 1 n (k2 i + k2 j ) − [ 1 n ∑ i→j 1 2 (ki + kj) ] 2 , (24) whe... |

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161 |
The asymptotic number of labeled graphs with given degree sequences
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Citation Context ... comparison with networks with the same degree distribution. Models to generate networks with a given degree distribution, while being random in other aspects, have been proposed. Bender and Canfield =-=[48]-=- first proposed a model to generate random graphs with a pre-defined degree distribution called configuration model. Later, Molloy and Reed [49, 50] proposed a different method that produces multigrap... |