basic principles of graph theory

1. The number I of loops in an arbitrary undirected connected graph is related to the number of its edges L and vertices N: I = L + 1-N

2. the clustering coefficient C of a vertex is the ratio between the total number y of the edges connecting its nearest neighbors and the total number of all possible edges between all these nearest neighbors, C = 2y/(z(z-1)). Thus, the clustering coefficient for tree is zero.