To calculate the total number of possible pairings of stubs between node i and node j, we multiply their degrees together:
Total possible pairings = k_i * k_j
To calculate the probability of a stub from node i being connected to a particular stub in the model, we divide the total number of edges m by the total number of possible pairings:
ppair = m / (k_i * k_j)
Suppose that node i has degree ki and node j has degree kj in a Configuration model with n nodes and total number of edges m.
What is the total number of possible pairings of stubs between these two nodes? (Use k_i for ki and k_j for kj.)
Suppose that we have selected a stub from node i, what is the probability of it being connected to a particular stub in the model? (Use m for m.)
ppair= ?
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