Calculations of System Difference and Average Connectedness in a graph. A) Representation of a directed, binary system in graph form. (B) The same system's corresponding connection matrix where rows represent outputs and columns represent inputs. A nonzero value in A
indicates the presence of a connection from node i to node j, and a value of zero indicates no connection. (C) Illustration of the concept of reachability. A node is reachable from another node if a path can be found between them. Node 4 can reach node 2 by passing through node 1. Node 2 cannot reach node 4. Average Connectedness is the average node reachability of the graph (that is, the number of pairs of nodes A and B - such that B is reachable from A - divided by the number of nodes). (D) The central calculation of System Difference (SD): non-overlap. When comparing the output structure of node 1 to that of node 3, we must define sets representing each node’s outputs. Those sets can then be compared to find the number of different entries (or non-overlap) between them. SD is the average non-overlap for all combinations of two nodes in the graph.