Monitoring a labeled degree-corrected stochastic block model

The stochastic block model (SBM) is a random graph model that focuses on partitioning the nodes into blocks or communities. A degree-corrected stochastic block model (DCSBM) considers degree heterogeneity within nodes. Investigation of the type of edge label can be useful for studying networks. We have proposed a labeled degree-corrected stochastic block model (LDCSBM), added the probability of the occurrence of each edge label, and monitored the behavior of this network. The LDCSBM is a dynamic network that varies over time; thus, we applied the monitoring process to both the US Senate voting network and simulated networks by defining structural changes. We used the Shewhart control chart for detecting changes and studied the effect of Phase I parameter estimation on Phase II performance. The efficiency of the model for surveillance has been evaluated using the average run length for estimated parameters.