An adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not. In the special case of a finite simple graph, the adjacency matrix is a (0,1)-matrix with zeros on its diagonal.

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How to measure the similarity between two weighted graphs？

I have two undirected graph networks and each edge of these networks are weighted through the Pearson Correlation Coefficient values.(Both of these networks have same nodes) I would like to quantify ...
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isomorphic adjacency matrices to one matrix

I need to generate lots of graphs to train my code. But it didn't have any impact if training graphs are isomorphic. So I need to eliminate isomorphic graphs to save time. For this reason, now I'm ...
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Spanning forests of bipartite graphs and distinct row/column sums of binary matrices

Let $F_{m,n}$ be the set of spanning forests on the complete bipartite graph $K_{m,n}$. Let $$S_{m,n} = \{(r(M), c(M)), M \in B_{m,n} \}$$ where $B_{m,n}$ is the set of $m \times n$ binary matrices ...
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Suppose $G_1$ and $G_2$ are two finite undirected simple graphs, such, that their adjacency matrices are conjugate over $\mathbb{Z}_2$ (as their only possible entries are always either $0$ or $1$, we ...
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Calculating the Distance Matrix from Adjacency Matrix

How would I calculate the distance matrix of a connected, simple and undirected graph from the adjacency matrix? I have 56 nodes, if that is helpful, and would need to the answer to return an array. ...
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Proof and notations

I was reading this proof, and I do not know what does E stands for, could you help me please? Theorem: Raising an adjacency matrix A of simple graph G to the n-th power gives the number of n-length ...