Fig 1.
Motifs in different contexts (right column) and example systems (left column). (A) Checkerboard motif. For example, 4 species (A–D) occupy 5 islands (I1–I5). The checkerboard motif highlighted in red represents 2 species that do not co-occur on the same island (here, B appears on I5 but D does not, and conversely, D appears on I3 but B does not), suggestive of competitive interactions. (B) Triadic clustering motif. For example, the motif represents cases in which an individual’s connected friends are also connected with each other, having significance, for example, in social networks and epidemiological contact networks. (C) Feed-forward loop motif. For example, a circuit in gene transcription networks, in which DNA target β can be activated only through simultaneous binding of two transcription factors A and B, and in which B depends on A initially binding to DNA targets α and β, suggesting regulatory control on transcription.
Fig 2.
Randomizing matrices with switches.
Switches between one checkerboard configuration to another (see 0s and 1s marked in red) leave the row and column sums of the matrix unchanged. One method to generate a set of random samples from the universe of all possible matrices U(r,c) simply requires implementing a large set of switches to randomly chosen checkerboard configurations in the adjacency matrix.