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Sci Rep. 2016 Feb 25;6:22057. doi: 10.1038/srep22057.

Small-World Propensity and Weighted Brain Networks.

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Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104 USA.
US Army Research Laboratory, Aberdeen Proving Ground, MD 21005, USA.
Department of Mathematics and Computational and Data-Enabled Science and Engineering Program, University at Buffalo, Buffalo, NY 14260 USA.
Department of Biomedical Engineering, Johns Hopkins University, Baltimore, MD 21218 USA.
Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA 19104 USA.


Quantitative descriptions of network structure can provide fundamental insights into the function of interconnected complex systems. Small-world structure, diagnosed by high local clustering yet short average path length between any two nodes, promotes information flow in coupled systems, a key function that can differ across conditions or between groups. However, current techniques to quantify small-worldness are density dependent and neglect important features such as the strength of network connections, limiting their application in real-world systems. Here, we address both limitations with a novel metric called the Small-World Propensity (SWP). In its binary instantiation, the SWP provides an unbiased assessment of small-world structure in networks of varying densities. We extend this concept to the case of weighted brain networks by developing (i) a standardized procedure for generating weighted small-world networks, (ii) a weighted extension of the SWP, and (iii) a method for mapping observed brain network data onto the theoretical model. In applying these techniques to compare real-world brain networks, we uncover the surprising fact that the canonical biological small-world network, the C. elegans neuronal network, has strikingly low SWP. These metrics, models, and maps form a coherent toolbox for the assessment and comparison of architectural properties in brain networks.

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