Row and Column Sums of Adjacency Matrix of Undirected Graph equals Vertex Degree

Theorem

Let $G$ be an undirected graph.

Let $\mathbf M$ be the adjacency matrix for $G$.

The row sums and column sums of the rows and columns of $\mathbf M$ are equal to the degrees of the corresponding vertices of $G$.

Proof

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Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): adjacency matrix
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): adjacency matrix