Fig. 1.

Motifs and alignment in topological networks. (a) A randomly chosen connected subgraph is likely to be a tree; i.e., it has the number of internal links equal to its number of nodes minus 1. (b) Putatively functional subgraphs are distinguished by internal loops, i.e., by a higher number of internal links. (c) An alignment of three subgraphs with four nodes each. Each node carries an index α = 1, 2, 3 labeling its subgraph and an index i = 1, 2, 3, 4 given by the order of nodes within the subgraph. Nodes with the same index i are joined by dashed lines, defining a one-to-one mapping between any two subgraphs. Network links are shown as solid lines (with their arrows suppressed for clarity). (d) The consensus pattern of this alignment. Each link occurs with a likelihood c̄_ij indicated by the gray scale.