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Additional Issues for Bipartite Networks

It is worth emphasizing some principal differences between two- and onemode networks. The fact that we have two different types of nodes means that we have two distinct degree distributions, and if we are interested in modeling the degrees of nodes, we have to assume an ERGM that goes beyond the Bernoulli assumption in terms of dependence. Furthermore, it is important to keep in mind that the nodes are actually of different types when interpreting a model. Sometimes one type of node is truly constituent, one mode being constituted by a collection of the other type of node. Are dependencies between, say, corporate boards or a property of the boards, or because the boards are made up of the same directors? On occasion, we may use the A-P ties as proxies of underlying A-A or P-P ties. This is not to say that projecting A-P ties into their one-mode A-A or P-P projection is preferable. If anything, it can be shown that these projections give rise to spurious clustering and dependencies in the onemode projections that are mere artefacts of the projection (Wang, Sharpe, Robins & Pattison, 2009). Current research into multilevel networks (Lazega et al., 2008) attempts to parse out the unique contribution of different types of ties between different types of nodes to the overall network structure.

In many research contexts, there is one type of node that per definition must have ties present. It may, for example, not make sense to consider a club without any constituent members (Niekamp et al., 2011). Such restrictions imposed on the structure by the nature of the network may make it difficult to fully capture the respective degree distributions. This may be solved by combining a variety of degree-based effects or by conditioning the inference on the condition that there are no isolates (e.g., as can be done in BPNet).

Although the boundary definition may be a difficult issue in bipartite networks and not have an optimal solution, it goes a long way to be aware of its consequences on the inference (Koskinen & Edling, 2010). Was the network sampled on one type of node, and how large of a fraction of each type of node was collected? Each consideration has a bearing on the degree of overlap between the neighborhoods (clustering) and the extent to which degree distributions are restricted. ERGM for bipartite networks does not have as long a history of research as ERGM for unipartite networks, and issues of model specification and inference are the target of much current research.

 
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