The correlation of metrics in complex networks with applications in functional brain networks

Li, C.; Wang, H.; De Haan, W.; Stam, C.J.; Van Mieghem, P.F.A.

doi:doi:10.1088/1742-5468/2011/11/P11018

The correlation of metrics in complex networks with applications in functional brain networks

Title

The correlation of metrics in complex networks with applications in functional brain networks

Author

Li, C.
Wang, H.
De Haan, W.
Stam, C.J.
Van Mieghem, P.F.A.

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Telecommunications

Date

2011-11-25

Abstract

An increasing number of network metrics have been applied in network analysis. If metric relations were known better, we could more effectively characterize networks by a small set of metrics to discover the association between network properties/metrics and network functioning. In this paper, we investigate the linear correlation coefficients between widely studied network metrics in three network models (B´arabasi–Albert graphs, Erd¨os–R´enyi random graphs and Watts–Strogatz small-world graphs) as well as in functional brain networks of healthy subjects. The metric correlations, which we have observed and theoretically explained, motivate us to propose a small representative set of metrics by including only one metric from each subset of mutually strongly dependent metrics. The following contributions are considered important. (a) A network with a given degree distribution can indeed be characterized by a small representative set of metrics. (b) Unweighted networks, which are obtained from weighted functional brain networks with a fixed threshold, and Erdös–Rényi random graphs follow a similar degree distribution. Moreover, their metric correlations and the resultant representative metrics are similar as well. This verifies the influence of degree distribution on metric correlations. (c) Most metric correlations can be explained analytically. (d) Interestingly, the most studied metrics so far, the average shortest path length and the clustering coefficient, are strongly correlated and, thus, redundant. Whereas spectral metrics, though only studied recently in the context of complex networks, seem to be essential in network characterizations. This representative set of metrics tends to both sufficiently and effectively characterize networks with a given degree distribution. In the study of a specific network, however, we have to at least consider the representative set so that important network properties will not be neglected.

Subject

neuronal networks (experiment)
network dynamics
random graphs
networks
computational neuroscience

To reference this document use:

http://resolver.tudelft.nl/uuid:e0285ddd-675d-4546-b01c-f8f5e1c86d81

DOI

https://doi.org/10.1088/1742-5468/2011/11/P11018

Publisher

IOP/SISSA

Embargo date

2012-05-25

ISSN

1742-5468