Figure 2

Strongly connected graphs and components. Outlines of hypothetical graphs are shown, omitting some vertices and edges and all labels. (A) A strongly connected graph in which any pair of vertices can be joined, both ways, by a path of contiguous edges in the same direction (central motif). (B) A graph that is not strongly connected can always be decomposed into maximal strongly connected sub-graphs, called strongly connected components (SCCs). The graph shown here has four SCCs demarcated by the dotted lines. In the macroscopic interpretation of one-dimensional chemistry, matter can only flow in one direction between SCCs, so that it eventually accumulates only on the terminal SCCs (marked with an asterisk). In the microscopic interpretation, microstates that are not in a terminal SCC have zero steady-state probability.