made easy test series

Question

Suppose A is a 12 by 9 incidence matrix from a connected (but unknown) graph with 9 nodes and 12 edges. The diagonal entries of $A^{T}.A$

give the number of edges into each node. Then, what is the sum of those diagonal entries ________.

Answer 1

The sum of the entries of $A^{T}A$ is the sum of the degrees of all of the nodes. As each edge hits exactly two nodes it will be counted twice, so the sum of the diagonal entries is 24.