Topological Generalizations of network motifs

Network motif provides a way to uncover the basic building blocks of most complex networks. This task usually demands high computer processing, specially for motif with 5 or more vertices. This paper presents an extended methodology with the following features: (i) search for motifs up to 6 vertices, (ii) multithread processing, and a (iii) new enumeration algorithm with lower complexity. The algorithm to compute motifs solve isomorphism in $O(1)$ with the use of hash table. ...

A deluge of new data on social, technological and biological networked systems suggests that a large number of interactions among system units are not limited to pairs, but rather involve a higher number of nodes. To properly encode such higher-order interactions, richer mathematical frameworks such as hypergraphs are needed, where hyperlinks describe connections among an arbitrary number of nodes. Here we introduce the concept of higher-order motifs, small connected subgraph...

The distribution of motifs in random hierarchical networks defined by nonsymmetric random block--hierarchical adjacency matrices, is constructed for the first time. According to the classification of U. Alon et al of network superfamilies by their motifs distributions, our artificial directed random hierarchical networks falls into the superfamily of natural networks to which the class of neuron networks belongs. This is the first example of ``handmade'' networks with the mot...

The cell cycle is a tightly controlled process, yet its underlying genetic network shows marked differences across species. Which of the associated structural features follow solely from the ability to impose the appropriate gene expression patterns? We tackle this question in silico by examining the ensemble of all regulatory networks which satisfy the constraint of producing a given sequence of gene expressions. We focus on three cell cycle profiles coming from baker's yeas...

Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the underlying reasons for the variable quantity of different subgraph types, their propensity to form clusters, and their relationship with the networks' global organization remain poorly understood. Here we show that a network's large-scale topologica...

Complex networks have been characterised by their specific connectivity patterns (network motifs), but their building blocks can also be identified and described by node-motifs---a combination of local network features. One technique to identify single node-motifs has been presented by Costa et al. (L. D. F. Costa, F. A. Rodrigues, C. C. Hilgetag, and M. Kaiser, Europhys. Lett., 87, 1, 2009). Here, we first suggest improvements to the method including how its parameters can b...

Studying the topology of so-called {\em real networks}, that is networks obtained from sociological or biological data for instance, has become a major field of interest in the last decade. One way to deal with it is to consider that networks are built from small functional units called {\em motifs}, which can be found by looking for small subgraphs whose numbers of occurrences in the whole network of interest are surprisingly high. In this paper, we propose to define motifs ...

It may be possible to discover much of the organization of synaptic connections in nervous systems by designing simple logic circuits that can perform a single, biologically advantageous function. This method has led to neuronal networks that can generate neural correlates of phenomena central to color vision, olfaction, short-term memory, and brain waves. One of the network designs is a family of general information processors that exhibit major features of cerebral cortex p...

We generalize a sampling algorithm for lattice animals (connected clusters on a regular lattice) to a Monte Carlo algorithm for `graph animals', i.e. connected subgraphs in arbitrary networks. As with the algorithm in [N. Kashtan et al., Bioinformatics 20, 1746 (2004)], it provides a weighted sample, but the computation of the weights is much faster (linear in the size of subgraphs, instead of super-exponential). This allows subgraphs with up to ten or more nodes to be sample...

Gene regulatory networks constitute the first layer of the cellular computation for cell adaptation and surveillance. In these webs, a set of causal relations is built up from thousands of interactions between transcription factors and their target genes. The large size of these webs and their entangled nature make difficult to achieve a global view of their internal organisation. Here, this problem has been addressed through a comparative study for {\em Escherichia coli}, {\...