First of all, do you know what is the complement of undirected graph? That is, all nodes are reserved, there are edges between two points, the complementary graph has no edges, the complementary graph has edges, and the number of edges of the original graph+the number of edges of the complementary graph is equal to c (5 5,2) =10 ... So finding the maximum number of edges of an undirected graph is finding the minimum number of edges of the complementary graph. Since a complementary graph is connected, it has at least four edges (trees).

In addition, this problem has a premise, that is, undirected simple graph, that is, there is no self-ring and no parallel edges.

If you have any questions, please add them, and if you are satisfied, please adopt them ~