Local clustering coefficient for two-mode networks
January 6, 2010 at 6:29 pm 4 comments
Similar to the motivation of the global clustering coefficient that I proposed in Clustering in two-mode networks, the local clustering coefficient is biased if applied to a projection of a two-mode network. It is biased in the sense that the randomly expected value is not obtained on the projection of a random two-mode network. To overcome this methodological bias, I redefine the local clustering coefficient for two-mode networks. The new coefficient is a mix between the global clustering coefficient for two-mode networks and Barrat’s (2004) local coefficient for a weighted one-mode network. The coefficient is tested on Davis’ (1940) Southern Women dataset.
Entry filed under: Network thoughts. Tags: actors, affiliation networks, arcs, bipartite networks, clustering coefficient, complex networks, edges, embeddedness, graphs, Links, local, network, nodes, social network analysis, strength of ties, ties, two-mode networks, valued networks, vertices, weighted networks.
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Tore Opsahl 
1.
Matthieu Latapy | February 11, 2011 at 10:22 pm
Similar measures and other notions for the analysis of two-mode (i.e., bipartite, i.e., affiliation) networks are also proposed in:
Basic Notions for the Analysis of Large Two-mode Networks
by Matthieu Latapy, Clémence Magnien and Nathalie Del Vecchio,
Social Networks (2008), vol. 30, no1, pp. 31-48.
2.
Tore Opsahl | February 12, 2011 at 3:59 pm
Matthieu,
Thank you for the reference. In an updated paper that’s already under revision, that reference is well incorporated.
Best,
Tore
3.
COLIN | April 15, 2011 at 1:57 pm
Dear Tore,
Have you seen the following publications:
zhang et al (2008) Clustering coefficient and community structure of bipartite networks. Physica A
and cited in
Beguerisse Díaz et al (2010) for popularity in bipartite networks. Chaos. 20, 043101
May ask your opinion on these and the difference between them and the above?
C
4.
Tore Opsahl | April 19, 2011 at 8:26 pm
Colin,
Thanks for the feedback. Zhang et al’s paper is interesting, and is commented on in the updated version of the paper that this blog post is based on. The main difference between their measure and the above measure is that they use 4-cycles, and therefore only measure two primary nodes tendency to for, repeated ties between themselves. The purpose of the above measure is to measure closure among three primary nodes (i.e., among a group).
Tore