Quantifying community evolution in temporal networks

When we detect communities in temporal networks it is important to ask questions about how they change over time. Adjusted mutual information (AMI) has been used to measure the similarity of communities when the nodes on a network do not change. We propose two extensions, namely, Union-Adjusted Mutual Information (UAMI) and Intersection-Adjusted Mutual Information (IAMI). UAMI and IAMI evaluate the similarities of community structures when nodes are added or removed. Experiments show that these methods are effective in dealing with temporal networks with the changes in the set of nodes, and can capture the dynamic evolution of community structure in both synthetic and real temporal networks. This study not only provides a new similarity measurement method for network analysis but also deepens the understanding of community change in complex temporal networks.