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

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.

Title	A new measure based on degree distribution that links information theory and network graph analysis
Creator	Liew, Chun Wai
	McGranaghan, M. F.
	Willey, A.
	Hadley, M. W.
	Reynolds, Elaine R.
Publisher	Neural Systems and Circuits
Academic Department	Biology
Academic Department	Computer Science
Division	Natural Sciences
Organization	Lafayette College
Date Issued	2012
Date Available	2015-03-06T18:18:32Z
Type	Article
Language	English
Keyword	Degree distribution
	Information integration theory
	Graph theory
	Neural networks
	Small world properties
Bibliographic Citation	Hadley, M. W., et al. (2012) "A new measure based on degree distributionthat links information theory and network graph analysis." Neural Systems and Circuits 2: 7.
Standard Identifier	DOI 10.1186/2042-1001-2-7
Standard Identifier	Handle 10385/1726
Permalink	http://hdl.handle.net/10385/1726
Rights Statement	Creative Commons - Attribution
Rights Holders	Liew, Chun Wai
	McGranaghan, M. F.
	Willey, A.
	Hadley, M. W.
	Reynolds, Elaine R.