Graph Polynomials#

Provides algorithms supporting the computation of graph polynomials.

Graph polynomials are polynomial-valued graph invariants that encode a wide variety of structural information. Examples include the Tutte polynomial, chromatic polynomial, characteristic polynomial, and matching polynomial. An extensive treatment is provided in [1].

For a simple example, the charpoly method can be used to compute the characteristic polynomial from the adjacency matrix of a graph. Consider the complete graph K_4:

>>> import sympy
>>> x = sympy.Symbol("x")
>>> G = nx.complete_graph(4)
>>> A = nx.adjacency_matrix(G)
>>> M = sympy.SparseMatrix(A.todense())
>>> M.charpoly(x).as_expr()
x**4 - 6*x**2 - 8*x - 3

Y. Shi, M. Dehmer, X. Li, I. Gutman, “Graph Polynomials”


Returns the Tutte polynomial of G


Returns the chromatic polynomial of G