  Community detection in networks is the process of identifying unusually
well-connected sub-networks and is a central component of many applied network
analyses. The paradigm of modularity optimization stipulates a partition of the
network's vertices which maximizes the difference between the fraction of edges
within groups (communities) and the expected fraction if edges were randomly
distributed. The modularity objective function incorporates the network's
topology exclusively and has been extensively studied whereas the integration
of constraints or external information on community composition has largely
remained unexplored. We impose a penalty function on the modularity objective
function to regulate the constitution of communities and apply our methodology
in identifying health care communities (HCCs) within a network of hospitals
such that the number of cardiac defibrillator surgeries performed within each
HCC exceeds a minimum threshold. This restriction permits meaningful
comparisons in cardiac care among the resulting health care communities by
standardizing the distribution of cardiac care across the hospital network.
