Topological Generalizations of network motifs

A $k$-motif (or graphlet) is a subgraph on $k$ nodes in a graph or network. Counting of motifs in complex networks has been a well-studied problem in network analysis of various real-word graphs arising from the study of social networks and bioinformatics. In particular, the triangle counting problem has received much attention due to its significance in understanding the behavior of social networks. Similarly, subgraphs with more than 3 nodes have received much attention rec...

Because of the huge number of graphs possible even with a small number of nodes, inference on network structure is known to be a challenging problem. Generating large random directed graphs with prescribed probabilities of occurrences of some meaningful patterns (motifs) is also difficult. We show how to generate such random graphs according to a formal probabilistic representation, using fast Markov chain Monte Carlo methods to sample them. As an illustration, we generate re...

We present a comparative analysis of large-scale topological and evolutionary properties of transcription networks in three species, the two distant bacteria E. coli and B. subtilis, and the yeast S. cerevisiae. The study focuses on the global aspects of feedback and hierarchy in transcriptional regulatory pathways. While confirming that gene duplication has a significant impact on the shaping of all the analyzed transcription networks, our results point to distinct trends be...

Community definitions usually focus on edges, inside and between the communities. However, the high density of edges within a community determines correlations between nodes going beyond nearest-neighbours, and which are indicated by the presence of motifs. We show how motifs can be used to define general classes of nodes, including communities, by extending the mathematical expression of Newman-Girvan modularity. We construct then a general framework and apply it to some syn...

Central to the functioning of a living cell is its ability to control the readout or expression of information encoded in the genome. In many cases, a single transcription factor protein activates or represses the expression of many genes. As the concentration of the transcription factor varies, the target genes thus undergo correlated changes, and this redundancy limits the ability of the cell to transmit information about input signals. We explore how interactions among the...

Network structures are extremely important to the study of political science. Much of the data in its subfields are naturally represented as networks. This includes trade, diplomatic and conflict relationships. The social structure of several organization is also of interest to many researchers, such as the affiliations of legislators or the relationships among terrorist. A key aspect of studying social networks is understanding the evolutionary dynamics and the mechanism by ...

The activation/repression of a given gene is typically regulated by multiple transcription factors (TFs) that bind at the gene regulatory region and recruit RNA polymerase (RNAP). The interactions between the promoter region and TFs and between different TFs specify the dynamic responses of the gene under different physiological conditions. By choosing specific regulatory interactions with up to three transcription factors, we designed several functional motifs, each of which...

We present a theoretical formalism to study steady state information transmission in type 1 coherent feed-forward loop motif with an additive signal integration mechanism. Our construct allows a two-step cascade to be slowly transformed into a bifurcation network via a feed-forward loop which is a prominent network motif. Utilizing a Gaussian framework, we show that the feed-forward loop motif harnesses the maximum amount of Shannon mutual information fractions constructed be...

Topological features of gene regulatory networks can be successfully reproduced by a model population evolving under selection for short dynamical attractors. The evolved population of networks exhibit motif statistics, summarized by significance profiles, which closely match those of {\it E. coli, S. cerevsiae} and {\it B. subtilis}, in such features as the excess of linear motifs and feed-forward loops, and deficiency of feedback loops. The slow relaxation to stasis is a ha...

In the last decade, network science has shed new light both on the structural (anatomical) and on the functional (correlations in the activity) connectivity among the different areas of the human brain. The analysis of brain networks has made possible to detect the central areas of a neural system, and to identify its building blocks by looking at overabundant small subgraphs, known as motifs. However, network analysis of the brain has so far mainly focused on anatomical and ...