(A) A directed network. The circles represent nodes in the network. Arrows represent directed edges connecting between nodes. Edge weights are denoted by Arabic numerals attached to the edge. (B) A binary matrix representation of the directed network. If there exists a directed edge from node i to node j in the matrix, then cell aij = 1. Otherwise, aij = 0. The number of ingoing edges (IN degree) of each node is defined as the sum of the corresponding column. The number of outgoing edges (OUT degree) of each node is the sum of the corresponding row. (C) A weighted matrix representation of the directed network. Cells in the matrix correspond to the edge weight of edges connecting between nodes i and j. The column sums are the total edge weight of ingoing edges. The row sums are the total edge weight of outgoing edges.
