Correlation between graphs with an application to brain network analysis

Identification of causality in genetics and neuroscience

“…Thus, statistical analysis over graphs can be performed based solely on their spectral radii. Notably, Fujita et al (2017) already used the spectral radius to construct a framework for identifying correlation between samples of graphs. They propose to test correlation between graphs by testing the Spearman's rank correlation between the samples of the respective spectral radii.…”

“…Based on spectral graph theory and under the assumption that graphs are generated by mathematical models whose parameters are random variables, Fujita et al (2017) present a new notion of dependence among random graphs. The treatment of the parameters as random variables is common in Bayesian data analysis.…”

“…The idea is that the parameter value of the model used to generate the graph is drawn from the prior distribution (Gelman et al, 2013). Specifically, Fujita et al (2017) define that two graphs are independent when the random variables representing their parameters are independent. Thus, a simple way to test whether two graphs are independent is to test the probabilistic dependence between the parameters of their models.…”

“…By leveraging this relation between spectral radius and the model parameters, Fujita et al (2017) propose to test correlation between two samples of graphs by testing the Spearman's rank correlation between the samples of the respective spectral radii. The Spearman's rank correlation coefficient is defined as the Pearson correlation coefficient between the ranked variables.…”

“…Thus, inspired by Fujita et al (2017), we present in Section 3.2.2 a method that identifies Granger causality among time series of undirected graphs by fitting a VAR model on the time series of the ranked spectral radii. We call it gVAR, which stands for VAR model for graphs.…”