Thursday, August 8, 2019
Wednesday, August 7, 2019
Yuan clearly used weighted matrix, and j->i as direction. So, column to row indicate direction?
Wikipedia, “In directed graphs, the in-degree of a vertex can be computed by summing the entries of the corresponding column, and the out-degree can be computed by summing the entries of the corresponding row.” The question now is does i->j and j->i matters? It can be tested using a star shaped network with outward and inwarding arrows. A quick exam on these show both star networks should have the same number of minimal control nodes. Well, eigen values of a matrix and its transpose are the same, see https://yutsumura.com/eigenvalues-of-a-matrix-and-its-transpose-are-the-same/.
So, i->j and j->i does not matter! This is somewhat shocking to me.