Functional connectivity brain network analysis through network to signal transform based on the resistance distance

Functional connectivity brain networks have been shown to demonstrate interesting complex network behavior such as small-worldness. Transforming networks to time series has provided an alternative way of characterizing the structure of complex networks. However, previously proposed deterministic methods are limited to unweighted graphs. In this paper, we propose to employ the resistance distance matrix of weighted graphs as the distance matrix for transforming networks to signals based on classical multidimensional scaling. We present a framework for obtaining information about the network's structure through the mapped signals and recovering the original network using properties of the resistance matrix. Finally, the proposed method is applied to characterizing functional connectivity networks constructed from electroencephalogram data.