Fig. 3
From: Stochastic block models with multiple continuous attributes
Detectability Analysis in Synthetic Example. To understand how attribute information can be combined with connectivity to assign nodes to communities accurately, we generated synthetic networks for within-probabilities of pin between 0.05 and 0.3 with corresponding pout or between-community probabilities such that the mean degree of the network was 20. For each of these synthetic networks, we used the attributes from the analysis in Fig. 2 to fit the attributed SBM. Here, we plot the correctness of the node-to-community assignment with normalized mutual information using the partition obtained from regular SBM (blue) and the partition under the attributed SBM model fit (pink). For each combination of pin and pout, we generated 10 networks and hence the bands around the points denote standard deviation. Incorporating attributes with the attributes stochastic block model improves results, particularly near and below the detectability limit, and appears to smooth out the sharp phase transition