It is well recognized that hypergraphs can be represented as factor graphs to some extent.
But something plagued me is that, when converted to a factor graph, how is the degree of a node in the factor graph calculated? For example, when a node i in a factor graph is connected to a factor node with cardinality 5 in a hypergraph, is the degree of node i considered as 5? Or is it regarded as 1?
Can anyone explain this for me? I appreciate it a lot. And thanks for your time.
In your example, the degree is 1.
For hypergraph, the degree is just the number of hyperedges the node is incident to, which is equal to the degree of the corresponding node in the factor graph. In the factor graph, you may also consider the degree of factor nodes, which follows the normal definition of degree for ordinary graphs.
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