Let A be the adjacency matrix of an undirected network and 1 be the column vector whose elements are all 1. In terms of these quantities, write expressions for;

a) the vector k whose elements are the degrees ki of the vertices;

b) the number m of edges in the network;

c) the matrix N whose element Nij is equal to the number of common neighbors of vertices i and j;

d) the total number of triangles in the network, where a triangle means three vertices, each connected by edges to both of the others