Small Worlds Among Interlocking Directors: Network Structure and Distance in Bipartite Graphs

We describe a methodology to examine bipartite relational data structures as exemplified in networks of corporate interlocking. These structures can be represented as bipartite graphs of directors and companies, but direct comparison of empirical datasets is often problematic because graphs have different numbers of nodes and different densities. We compare empirical bipartite graphs to simulated random graph distributions conditional on constraints implicit in the observed datasets. We examine bipartite graphs directly, rather than simply converting them to two 1-mode graphs, allowing investigation of bipartite statistics important to connection redundancy and bipartite connectivity. We introduce a new bipartite clustering coefficient that measures tendencies for localized bipartite cycles. This coefficient can be interpreted as an indicator of inter-company and inter-director closeness; but high levels of bipartite clustering have a cost for long range connectivity. We also investig...

• Type: Journal
• Year: 2004
• Where: CMOT
• Authors: Garry Robins, Malcolm Alexander
• Keywords: Bipartite Graphs, CMOT 2004, Empirical Bipartite Graphs, Graph Distributions