Homophily and nationality assortativity among the most cited researchers' social network

It is well known that individuals in social networks tend to exhibit homophily, the preference of people to associate with others from the same social group or type. Graph assortativity or Modularity is the most accepted measure for the homophily level of the whole network. It is well defined for simple networks where each node has a single type, and edges are unweighted. In this work, we extend modularity and assortativity in several ways. First, we define type assortativity which measures the homophily level of each type and enable the comparison between types of different size within the network. Second, we extend the measures to the case of nodes with multiple types and weighted edges. We evaluate our definitions on a weighted, research collaboration, social network between the most cited authors in the ACM digital library. We use nationality-based multiple types where a author can belong to multiple nationalities. While nationality-based homophily is trivial when the network is large (based on local research at universities) our empirical results show that even for the top 1000 authors a high level of nationality-based homophily exists, and different nationalities exhibit a different level of homophily.