Measuring the strength of networks of teams: Metrics and properties

A Network of Teams (NoT) is a set of overlapping teams working toward a common goal. NoTs arise in several contexts such as large software projects, sensors cooperating for target tracking, and terrorist cell networks. Modeling a NoT as a simplicial complex, we consider the problem of quantifying the strength of a NoT using metrics based purely on its structure. While the design of a metric clearly depends on the context in question, most applications require the metric to be monotonic. We define three kinds of monotonicity - weak, team, and structural - depending upon whether we add/remove nodes, entire teams, or facets, respectively We propose seven metrics and analyze their monotonicity, both mathematically and experimentally. Specifically, we prove that some metrics or monotonic, and show that some or not by providing counter examples. For nonmonotonic metrics, we generate random simplicial complexes using a number of models, and estimate the fraction of cases for which a metric is not monotonic.