Title

Reciprocity in Directed Networks

Document Type

Article

Publication Date

4-2016

Keywords

Reciprocity, Entropy, Free energy, Directed network, Exponential random graph

Organizational Units

College of Natual Science and Mathematics, Mathematics

Abstract

Reciprocity is an important characteristic of directed networks and has been widely used in the modeling of World Wide Web, email, social, and other complex networks. In this paper, we take a statistical physics point of view and study the limiting entropy and free energy densities from the microcanonical ensemble, the canonical ensemble, and the grand canonical ensemble whose sufficient statistics are given by edge and reciprocal densities. The sparse case is also studied for the grand canonical ensemble. Extensions to more general reciprocal models including reciprocal triangle and star densities will likewise be discussed.

Publication Statement

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