Reciprocity in directed networks

Lingjiong Zhu; Mei Yin

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Reciprocity in directed networks

Mei Yin, Lingjiong Zhu

Statistical Mechanics · Submitted 6 Dec 2014

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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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.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	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.	background 1.00	0.03	0.03	asserted 1.00
s1	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.	contribution 0.88	0.90	0.08	asserted 0.86
s2	The sparse case is also studied for the grand canonical ensemble.	contribution 0.92	0.82	0.04	asserted 0.97
s3	Extensions to more general reciprocal models including reciprocal triangle and star densities will likewise be discussed.	future work 0.55	0.38	0.04	asserted 0.57

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Original 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.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it

Cites it as background 1 paper

For exponential random graphs, see [ref] .

On the lower tail variational problem for random graphs · Background · 1.00

What it cites · 10 sentences without a confident label

Uses the method or tool of 1 paper

Solving for $g(x,y)$ and then integrating over $y$, we get [equation] Following similar arguments as in Kenyon et al. [ref] , we conclude that $d(x)$ can take only finitely many values.

Multipodal Structure and Phase Transitions in Large Constrained Graphs · Further discussion · 0.84

Cites as background 3 papers

As in Aristoff and Zhu [ref] , Kenyon and Yin [ref] and Zhu [ref] , we are interested in the asymptotic features of constrained models.

Asymptotic structure and singularities in constrained directed graphs · The canonical ensemble · 0.90
As in Aristoff and Zhu [ref] , Kenyon and Yin [ref] and Zhu [ref] , we are interested in the asymptotic features of constrained models.

On the asymptotics of constrained exponential random graphs · The canonical ensemble · 0.90
As in Aristoff and Zhu [ref] , Kenyon and Yin [ref] and Zhu [ref] , we are interested in the asymptotic features of constrained models.

Asymptotic Structure of Constrained Exponential Random Graph Models · The canonical ensemble · 0.90

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