where d(i) is the degree of node i, P(v, w) is the set of the all nodes visited en route on the shortest path from node v to node w, excluding the source node v and the target destination node w, and F (c) is the signal transduction behavior function. When v = w and distance (v, w) = 0, we define S (v → w) = d (v). The numerator of the first term in the right hand side of Equation 2 represents the degree of the source node v, and the denominator represents the dissipation on each visiting node on the shortest path from source node v to target node w. Our choice of the shortest path is motivated by the finding that the majority of flux prefers the path of least resistance in many physicochemical and biological systems. There can be more than one shortest path between a node pair in a network. STM chooses the least resistant path, which has the lowest resistance calculated by ∏i ∈ P (v, w) d (i) in Equation 2, out of several tying shortest paths if there are more than one shortest path between a node pair. There also can be more than one least resistant path among several tying shortest paths. Choosing any one path out of several tying least resistant paths makes no difference in measuring the signal transduction quantity as long as it is a least resistant path since the signal quantity computed by Equation 2 depends only on the resistance not on any other topological properties of intermediate visiting nodes on a path. So, the first term in the right hand side of Equation 2 represents the topological effect of source node v on target node w. The second term in the right hand side of Equation 2 represents the biological effect of source node v on target node w in the signal transduction view point. Therefore, the nodes that score the highest value on target node w will be the most influential nodes on node w biologically and topologically.