Talk:Graph power

A fact from Graph power appeared on Wikipedia's Main Page in the Did you know column on 4 March 2013 (check views). The text of the entry was as follows:

Did you know... that in the square of a graph, all vertices with a distance of no more than two in the original graph are adjacent?

A record of the entry may be seen at Wikipedia:Recent additions/2013/March. The nomination discussion and review may be seen at Template:Did you know nominations/Graph power.

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Weighted graph[edit]

Any references? If vertex A->B is weight a and vertex B->C is weight b, then the new edge A->C should be weight a+b?

Darcourse (talk) 16:48, 22 April 2020 (UTC)[reply]

I was wondering the same thing myself. I think the logical extension is that the weight of the edge A->C should be the minimum of weight(A->V) + weight(V->C) for all vertices V in the graph. If in your example, the only path from A to C is through B, then this minimum would be a+b as you say.

This definition happens to be a tropical matrix power. --Saforrest (talk) 11:11, 27 July 2020 (UTC)[reply]