2019-03-12 10:04:15 +0200 asked a question Number of neighbors of a set of vertices in a graph Hi all, I'd like to know how to get the number of vertices that are adjacent to a given set of vertices in a graph. I have the following skeleton: from sage.graphs.independent_sets import IndependentSets G=[some graph] J=IndependentSets(G)  And I would like to know the number of neighbors of x for each x in J (i.e., the number of vertices of G\x that are adjacent to some vertex in x). Ideally I would like something like: F=0 t=var('t') for x in J: N=number_of_neighbors(x) F += t^N F  If G is a four cycle then number_of_neighbors(x)=2 for any subset x of two vertices of G, and the polynomial F above should be 1+6t^2 (because there is the empty independent set, 4 independent sets of size 1 each with 2 neighbors, and 2 independent sets of size 2 each with 2 neighbors). I appreciate your help! 2019-03-12 10:04:15 +0200 asked a question Number of vertices of a set of vertices in a graph Hi all, I'd like to know how to get the number of vertices that are adjacent to a given set of vertices in a graph. I have the following skeleton: from sage.graphs.independent_sets import IndependentSets G=[some graph] J=IndependentSets(G) And I would like to know the number of neighbors of x for each x in J (i.e., the number of vertices of G\x that are adjacent to some vertex in x). Ideally I would like something like: F=0 t=var('t') for x in J: N=number_of_neighbors(x) F += t^N F If G is a four cycle then number_of_neighbors(x)=2 for any subset x of two vertices of G, and the polynomial F above should be 1+6t^2 (because there is the empty independent set, 4 independent sets of size 1 each with 2 neighbors, and 2 independent sets of size 2 each with 2 neighbors).