Abstract
BackgroundDetailed 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.ResultsWe 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.ConclusionsThe new network measure, SD, provides a link between high entropic structures and degree distributions as related to small world properties.
Highlights
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
Development of new variables We considered a number of options for generating variables that were computationally simple yet captured the properties of specialization and connectedness
We were looking for a metric that measured specialization and connectedness, and took into account that systems with an intermediate density of connections were likely to be the most complex in terms of information states
Summary
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. More complex measures look at patterns of connections: whether all the nodes of the system are closely connected or integrated (for example, path length - the minimum number of edges between nodes); or whether some parts of the graph might have clustered connections or hubs (for example, clustering coefficient - a measure of how related neighbors are in a graph). These metrics provide a way of analyzing networks and lay the groundwork for understanding them. Small world characteristics are found in many real world networks [11]
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