Editing Adjacency matrix (section)

===Variations===
An {{nowrap|{{math|(''a'', ''b'', ''c'')}}}}-adjacency matrix {{mvar|A}} of a simple graph has {{math|''A''<sub>''i'',''j''</sub> {{=}} ''a''}} if {{math|(''i'', ''j'')}} is an edge, {{mvar|b}} if it is not, and {{mvar|c}} on the diagonal. The [[Seidel adjacency matrix]] is a {{math|{{nowrap|(−1, 1, 0)}}}}-adjacency matrix. This matrix is used in studying [[strongly regular graph]]s and [[two-graph]]s.<ref>{{cite journal |last=Seidel |first=J. J. |title=Strongly Regular Graphs with (−1, 1, 0) Adjacency Matrix Having Eigenvalue 3 |journal=[[Linear Algebra and Its Applications|Lin. Alg. Appl.]] |volume=1 |issue=2 |pages=281–298 |year=1968 |doi=10.1016/0024-3795(68)90008-6 |doi-access= }}</ref>

The '''[[distance matrix]]''' has in position {{math|(''i'', ''j'')}} the distance between vertices {{mvar|v<sub>i</sub>}} and {{mvar|v<sub>j</sub>}}. The distance is the length of a shortest path connecting the vertices. Unless lengths of edges are explicitly provided, the length of a path is the number of edges in it. The distance matrix resembles a high power of the adjacency matrix, but instead of telling only whether or not two vertices are connected (i.e., the connection matrix, which contains [[Boolean algebra|Boolean values]]), it gives the exact distance between them.