The published version of one of my papers came out today. Its title is one of my favorites among all of the papers that I've ever written. Here are some details about the paper.
Title: Complex Networks with Complex Weights
Authors: Lucas Böttcher and Mason A. Porter
Abstract: In many studies, it is common to use binary (i.e., unweighted) edges to examine networks of entities that
are either adjacent or not adjacent. Researchers have generalized such binary networks to incorporate edge
weights, which allow one to encode node–node interactions with heterogeneous intensities or frequencies (e.g.,
in transportation networks, supply chains, and social networks). Most such studies have considered real-valued
weights, despite the fact that networks with complex weights arise in fields as diverse as quantum information,
quantum chemistry, electrodynamics, rheology, and machine learning. Many of the standard network-science
approaches in the study of classical systems rely on the real-valued nature of edge weights, so it is necessary
to generalize them if one seeks to use them to analyze networks with complex edge weights. In this paper, we
examine how standard network-analysis methods fail to capture structural features of networks with complex
edge weights. We then generalize several network measures to the complex domain and show that random-walk
centralities provide a useful approach to examine node importances in networks with complex weights.
1 day ago
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