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We are interested in the regression analysis of dynamical networks. Our goal is to predict real-valued function values from a given observation which is manifested as series of graphs. Every observation is described by a set of dependent variables that we want to predict using the dynamical graphs. These graphs change their edges over time, while the set of nodes is assumed to be constant. Such settings can be found in many real-world applications, e.g., communication networks, brain connectivity, microblogging. We apply several measures to every graph in the series to globally describe its evolution. The resulting multivariate time series is used to learn vector autoregressive (VAR) models. The parameters of these models can be used to correlate them with the dependent variables. The graph measures typically depend on the type of edges, i.e., weighted or unweighted. So do the VAR models and thus the regression results. In this paper we argue that it is beneficial to keep edge weights in this setting. To support this claim, we analyze electroencephalographic (EEG) networks from patients suffering from visual field defects. The edge weights are in the unit interval and might be thresholded. We show that dynamical network models for weighted edges lead to similar regression performances compared to those of unweighted graphs.

The Effects of Edge Weights on Correlating Dynamical Networks - Comparing Unweighted and Weighted Brain Graphs of nervus opticus Patients