Networks of Motifs from Sequences of Symbols

We introduce a method to convert an ensemble of sequences of symbols into a weighted directed network whose nodes are motifs, while the directed links and their weights are defined from statistically significant co-occurences of two motifs in the same sequence. The analysis of communities of networks of motifs is shown to be able to correlate sequences with functions in the human proteome database, to detect hot topics from online social dialogs, to characterize trajectories of dynamical systems, and it might find other useful applications to process large amounts of data in various fields.

Figure 1

The 3-motifs network of the human proteome. Nodes belonging to the same community are labeled by the same number and share the same color. Most of the communities can be associated to a functional domain as described in Table I in 21.

Figure 2

Standard map. Number of components in the 3-motifs networks (main figure) and the Lyapunov exponent (inset), as a function of the nonlinearity parameter $a$.