In the incidence matrix, each entry represents a particular edge that comes off of a particular vertex; there is a 1 if the edge connects to that vertex. So if you add up the entries of an entire row, you will count the number of edges that come off of that vertex. This is simply the degree of that vertex. --Dakinsey 09:41, 6 November 2008 (UTC)
This is only true if there is no loop involving the vertex represented by the row. If there is a loop, this sum is actually the degree of the vertex minus 1 (because each loop contributes twice towards the vertex degree).
--Asuleime 14:21, 6 November 2008 (UTC)
