Inclusivity enhances robustness and efficiency of social networks

Abstract

Many modern institutions seek to be inclusive, but the quantitative benefits of this goal are not always communicated effectively to stakeholders. To facilitate this important dialogue, we propose a simple model with which to grow, in the presence of a given level of inclusivity, networks which represent the structure of organisations. The model proceeds via an unweighted random walk in which inclusivity r is the maximum allowable separation between a new contact and the set of established contacts, which thus represents the maximum tolerable amount of novelty or “otherness”. The model can capture realistic small world and scale-free properties. In addition, the model fixes the limiting degree distribution, and particular parameter choices and initial conditions also fix clustering coefficient, and so allows the role of inclusivity to be isolated from these confounding factors. By considering this model, and also by randomly rewiring real networks in either an inclusive or an exclusive way, we show that, in comparison to exclusivity, inclusivity promotes unity (by decreasing modularity), efficiency and robustness. Increasing the ratio of the number of links to the number of nodes also enhances these qualities, as well as reducing their dependence upon inclusivity.