Volume: 102

We consider the network constraints on the bounds of the assortativity coefficient, which measuresthe tendency of nodes with the same attribute values to be interconnected. The assortativitycoefficient is the Pearson’s correlation coefficient of node attribute values across network edges andranges between -1 and 1. We focus here on the assortativity of binary node attributes and show thatproperties of the network, such as degree distribution and the number of nodes with each attributevalue place constraints upon the attainable values of the assortativity coefficient. We explore theassortativity in three different spaces, that is, ensembles of graph configurations and node-attributeassignments that are valid for a given set of network constraints. We provide means for obtainingbounds on the extremal values of assortativity for each of these spaces. Finally, we demonstratethat under certain conditions the network constraints severely limit the maximum and minimumvalues of assortativity, which may present issues in how we interpret the assortativity coefficient.