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Open Access Research

A new measure based on degree distribution that links information theory and network graph analysis

Michael W Hadley1, Matt F McGranaghan1, Aaron Willey2, Chun Wai Liew2 and Elaine R Reynolds1*

Author Affiliations

1 Neuroscience Program, Lafayette College, Easton, PA 18042, USA

2 Department of Computer Science, Lafayette College, Easton, PA 18042, USA

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Neural Systems & Circuits 2012, 2:7  doi:10.1186/2042-1001-2-7

Published: 24 June 2012

Abstract

Background

Detailed connection maps of human and nonhuman brains are being generated with new technologies, and graph metrics have been instrumental in understanding the general organizational features of these structures. Neural networks appear to have small world properties: they have clustered regions, while maintaining integrative features such as short average pathlengths.

Results

We captured the structural characteristics of clustered networks with short average pathlengths through our own variable, System Difference (SD), which is computationally simple and calculable for larger graph systems. SD is a Jaccardian measure generated by averaging all of the differences in the connection patterns between any two nodes of a system. We calculated SD over large random samples of matrices and found that high SD matrices have a low average pathlength and a larger number of clustered structures. SD is a measure of degree distribution with high SD matrices maximizing entropic properties. Phi (Φ), an information theory metric that assesses a system’s capacity to integrate information, correlated well with SD - with SD explaining over 90% of the variance in systems above 11 nodes (tested for 4 to 13 nodes). However, newer versions of Φ do not correlate well with the SD metric.

Conclusions

The new network measure, SD, provides a link between high entropic structures and degree distributions as related to small world properties.

Keywords:
Degree distribution; Graph theory; Information integration theory; Neural networks; Degree distribution; Small world properties