Cross-community affinity: A polarization measure for multi-community networks

This article introduces a heterophily-based metric for assessing polarization in social networks when different opposing ideological communities coexist. The proposed metric measures polarization at the node level and is based on a node's affinity for other communities. Node-level values can then be aggregated at the community, network, or any intermediate level, resulting in a more comprehensive map of polarization. We looked at our metric on the Polblogs network, the White Helmets Twitter interaction network with two communities, and the VoterFraud2020 domain network with five communities. Additionally, we evaluated our metric on different sets of synthetic graphs to confirm that it yields low polarization scores, as expected. We employed three ways to build synthetic networks: synthetic labeling, dK-series, and network models, in order to assess how the proposed measure behaves to various topologies and network features. Then, we compared our metric to two commonly used polarization metrics, Guerra's boundary polarization and the random walk controversy score. We also examined how our suggested metric correlates with two network metrics: assortativity and modularity.