Discovering communities through friendship
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Abstract
We introduce a new method for detecting communities of arbitrary size in an undirected weighted network. Our approach
is based on tracing the path of closest-friendship between nodes in the network using the recently proposed Generalized
Erdo¨s Numbers. This method does not require the choice of any arbitrary parameters or null models, and does not suffer
from a system-size resolution limit. Our closest-friend community detection is able to accurately reconstruct the true
network structure for a large number of real world and artificial benchmarks, and can be adapted to study the multi-level
structure of hierarchical communities as well. We also use the closeness between nodes to develop a degree of robustness
for each node, which can assess how robustly that node is assigned to its community. To test the efficacy of these methods,
we deploy them on a variety of well known benchmarks, a hierarchal structured artificial benchmark with a known
community and robustness structure, as well as real-world networks of coauthorships between the faculty at a major
university and the network of citations of articles published in Physical Review. In all cases, microcommunities, hierarchy of
the communities, and variable node robustness are all observed, providing insights into the structure of the network.