(Whitney) rank polynomial of an undirected graph
rankpoly(G, x, y)
undirected graph or network
rank variable in rank poly
corank variable in rank poly
Important: The networks package has been deprecated.Use the superseding command GraphTheory[RankPolynomial] instead.
When n⁡G = number of vertices, m⁡G = number of edges, and c⁡G = number of components, one defines rank(G) = n(G) - c(G) and corank(G) = m(G) - rank(G).
The rank polynomial is a sum over all subgraphs H of G of x^(rank(G) - rank(H)) y^corank(H).
The coefficient of xi⁢yj in the rank polynomial is thus the number of spanning subgraphs of G having i more components than G and having a cycle space of dimension j.
This routine is normally loaded via the command with(networks) but may also be referenced using the full name networks[rankpoly](...).
G ≔ complete⁡4:
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