Network constraints on the mixing patterns of binary node metadata
arXiv:1908.04588 · doi:10.1103/PhysRevE.102.062310
Abstract
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.
arXiv comment18 pages, 7 figures
References in corpus (12)
- Mixing patterns in networks
- The Anatomy of the Facebook Social Graph
- Social Structure of Facebook Networks
- The Majority Illusion in Social Networks
- The ground truth about metadata and community detection in networks
- Assessing the relevance of node features for network structure
- Homophily and minority size explain perception biases in social networks
- Gender Disparities in Science? Dropout, Productivity, Collaborations and Success of Male and Female Computer Scientists
- Multiscale mixing patterns in networks
- Zero Pearson Coefficient for Strongly Correlated Growing Trees
- Lower bound of assortativity coefficient in scale-free networks
- Structural Bounds on the Dyadic Effect