A directed weighted graph of N nodes can be represented by a NxN weighted adjacency matrix W = {wij}, where wij>0 is the weight associated to the directed arc from node i to node j, and in general wij≠wji. The most intuitive index of a graph is its total number of links. This value measures the overall level of connectivity within the system. The respective weighted version is the total network weight that is the sum of all arc weights in the graph. The out- and in-degree of node i are defined respectively as the number of out- and in-going arcs. The sum of weights of the out- and in-coming arcs of a node i are called out- and in-strength.
