Graph how many edges

And how this is related with combinatorics? Martin Sleziak It seems you did not notice the dates. My mistake. Add a comment. Active Oldest Votes.

Lagerbaer Lagerbaer 3, 2 2 gold badges 21 21 silver badges 28 28 bronze badges. Does that help? Aryabhata Aryabhata Community Bot 1. Ofir Ofir 7, 1 1 gold badge 25 25 silver badges 36 36 bronze badges. Change Language. Related Articles. Table of Contents. Save Article. Improve Article. Like Article. Python 3 implementation to. Write totEdge n ;.

Argue your position. That is what school is for, to argue with your teachers. How else are you going to learn independent thinking? You should figure out how to prove that your result is correct. Math is not a matter of opinion.

Andrej Bauer Andrej Bauer I included a proof, and when doing so discovered a flaw in my argument! And that is not surprising, given that we have a symmetry between the two disjoing subgraphs.

Featured on Meta. Now live: A fully responsive profile. For that, Consider n points nodes and ask how many edges can one make from the first point. Obviously, n-1 edges. Now how many edges can one draw from the second point, given that you connected the first point? Since the first and the second point are already connected, there are n-2 edges that can be done. And so on. So the sum of all edges is:.

If this is a multigraph, then there is no max limit. A complete graph is an undirected graph where each distinct pair of vertices has an unique edge connecting them. This is intuitive in the sense that, you are basically choosing 2 vertices from a collection of n vertices.

This is the maximum number of edges an undirected graph can have. Now, for directed graph, each edge converts into two directed edges. So just multiply the previous result with two. That gives you the result: n n In a directed graph having N vertices, each vertex can connect to N-1 other vertices in the graph Assuming, no self loop. Hence, the total number of edges can be are N N And this is achievable if we label the vertices 1,2, Each edge has been counted twice, hence the division by 2.

True if only any pair can have only one edge. Multiply by 2 otherwise.