Scale-free property of directed networks with two intrinsic node weights

Shigeo Shioda and Kazuhiro Nakamura

Physica A: Statistical Mechanics and its Applications, 2009, vol. 388, issue 15, 3249-3260

Abstract: This paper proposes a network model to understand the scale-free property of directed networks. The proposed model assigns two intrinsic variables (incoming and outgoing weights) to every node. A directed link is established from node i to node j if the sum of the outgoing weight of node i and the incoming weight of node j exceeds a predetermined threshold. The proposed model allows us to know the exact analytical expressions for degree distributions and clustering. We analytically find that the in-degree and out-degree distributions have power-law tails and their scaling exponents are controllable within the range (1,∞). The average clustering coefficient of nodes with out-degree (or in-degree) n also has a power-law tail as a function of n. We also find that the scaling exponent of the clustering coefficient depends on the correlation between incoming and outgoing weights.

Keywords: Scale free; Directed graph; Degree distribution; Cluster coefficient; Vertex intrinsic variable (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:388:y:2009:i:15:p:3249-3260

DOI: 10.1016/j.physa.2009.04.018

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