# Hypergraphs and bipartite graphs ?? Why must a link be defined as the connection between just two…

Hypergraphs and bipartite graphs ??

Why must a link be defined as the connection between just two nodes? Suppose eight papers are in the fields of physics or chemistry. Group membership, i.e., to which field a paper belongs, is presented as a hypergraph in Figure 8.22. Each dotted area is a group or a hyperedge, which is a generalization of an undirected edge to connect possibly more than two nodes. Papers 4 and 5 are “interdisciplinary” papers, so their nodes are contained in both hyperedges.

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(a) We can transform the hypergraph in Figure 8.22 into an undirected bipartite graph by introducing two more nodes, each representing one of the hyperedges, and linking a “standard” node to a “hyperedge” node if the former is contained in the corresponding hyperedge. Draw this bipartite graph.

(b) Define an incidence matrix B of size 2 × 8 with

where group 1 is “Physics” and group 2 is “Chemistry.” Write down B for this

graph.

(c) Compute the matrix BT B. What is its interpretation?

(d) Compute the matrix BBT. What is its interpretation?