Robustness of the Eigenvalue Test for Community Structure

Abstract

Networks can take on many different forms, such as the people from the University you attend. Within these networks, community structure may exist. This "community structure" refers to the clustering of nodes by a common characteristic. There are many algorithms to extract communities within a network. These methods depend on the assumption that structure exists within the network. Statistical tests have been proposed to test this assumption. In practice, networks may have measurement errors. This usually comes in the form of missing data or other faults. As a result, networks may not tell the full story at surface level and network structure often suffer from some type of error, as there may be nodes or edges absent from the data or ones that should not exist within the network. We wish to observe the effectiveness of the largest eigenvalue test for community structure when error is introduced into the network.