Efficient Community Re-creation in Multilayer Networks Using Boolean Operations

Networks are useful mathematical representations of systems of interrelated entities. In cases where the entities can be related via different factors, the models can be extended to form networks of networks or multilayer networks. However, analyzing multilayer networks can get increasingly more expensive as the number of layers increase. We address the problem of efficiently finding communities in multilayer networks. Communities are groups of tightly connected entities that indicate that entities in the group are similar. Here we demonstrate that given certain easily verifiable structural conditions, which we term as self preserving communities, we can use fundamental Boolean operations to combine the communities obtained from each network layer to obtain the communities over the entire multilayer network. Our approach, when applied to real-world datasets such as traffic accidents, shows that we can reduce the time to find communities in multilayer networks by over 40%. Our proposed technique makes several important contributions to the nascent area of multilayer networks. We present an elegant and low-cost method to combine results from multiple layers, without recomputing the combined layers. Our method also makes it easier to add and process new information at individual layers. Together, our approach addresses both the variety aspect of big data by handling multiple data types as well as the volume aspect by enabling fast analysis of data from multiple networks.