Structural bounds on the dyadic effect

The dyadic effect is a phenomenon that occurs when the number of links between nodes sharing a common feature is larger than expected if the features are distributed randomly on the network. In this article, we consider the case when nodes are distinguished by a binary characteristic. Under these circumstances, two independent parameters, namely dyadicity and heterophilicity are able to detect the presence of the dyadic effect and to measure how much the considered characteristic affects the network topology. The distribution of nodes characteristics can be investigated within a two-dimensional space that represents the feasible region of the dyadic effect, which is bound by two upper bounds on dyadicity and heterophilicity. Using some network structural arguments, we are able to improve such upper bounds and introduce two new lower bounds, providing a reduction of the feasible region of the dyadic effect as well as constraining dyadicity and heterophilicity within a specific range. Some computational experiences show the bounds effectiveness and their usefulness with regards to different classes of networks.