Shadow networks: Discovering hidden nodes with models of information flow

James P. Bagrow, Suma Desu, Morgan R. Frank, Narine Manukyan, Lewis Mitchell, Andrew Reagan, Eric E. Bloedorn, Lashon B. Booker, Luther K. Branting, Michael J. Smith, Brian F. Tivnan, Christopher M. Danforth, Peter S. Dodds, Joshua C. Bongard

Complex, dynamic networks underlie many systems, and understanding these networks is the concern of a great span of important scientific and engineering problems. Quantitative description is crucial for this understanding yet, due to a range of measurement problems, many real network datasets are incomplete. Here we explore how accidentally missing or deliberately hidden nodes may be detected in networks by the effect of their absence on predictions of the speed with which information flows through the network. We use Symbolic Regression (SR) to learn models relating information flow to network topology. These models show localized, systematic, and non-random discrepancies when applied to test networks with intentionally masked nodes, demonstrating the ability to detect the presence of missing nodes and where in the network those nodes are likely to reside.

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