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