AbstractReal world networks typically have large clustering coefficients. The clustering coefficient can be interpreted to be the result of a triangle closing mechanism. We have here enumerated cliques and maximal cliques in multiple networks to show that real world networks have a high number of large cliques. While triangles are more frequent than expected, large cliques are much more over-expressed, and the largest difference between real world networks and their random counterpart occurs in many networks at clique sizes of 5–7, and not at a size of 3. This does not result from the existence of few very large cliques, since a similar feature is observed when studying only maximal cliques (cliques that are not contained in other larger cliques). Moreover, when the large cliques are removed, triangles are often under-expressed.In all networks studied but one, all node members of large cliques produce a single connected component, which represent the central “core” of the network. The observed clique distribution can be explained by multiple models, mainly hidden variables model, such as the gravitation model, or the collapse of bipartite networks. These models can explain other properties of these networks, including the sub-graph distribution and the distance distribution of the networks. This suggests that node connectivity in real world networks may be determined by the similarity between the contents of the networks' nodes. This is in contrast with models of network formation that incorporate only the properties of the network, and not the internal properties of the nodes.

Genetic networks integrate the reported interactions between genes into a global view of the transcription regulation. These networks contain, beyond each specific interaction, the information flow between genes and groups of genes that determine the cellular response to different stimuli. The flow of information in such networks is based on the structure of the directed interactions paths, and is not obviously decipherable from the number of paths between genes in the network, which grows exponentially with the number of nodes. We show here that the directional large scale information flow in genetic networks can be understood by combining the cycle (closed walk in graph theory terms) length and distance distributions. These properties are highly sensitive to the effect of flipping the direction of a small number of random edges. Here we focus on cycles composed of back and forth minimal paths between a pair of nodes that we further denote as loops. Intra-cellular networks contain a surprisingly large number of long directed loops that can carry information through multiple components of the network, and in parallel a surprisingly small number of short loops. The direction of practically every edge affects the network’s loop length distribution and the flow of information in the network. Swapping the direction of even 2.5% of the edges in regulatory genetic networks from their target to their source drastically reduces the number of long directed loops. All other properties tested here, such as the clustering coefficient or the degree distributions, are practically not affected by a swap of even 50% of edges. We propose a model of information flow to explain this hyper-sensitivity of the loop length distribution to the direction of edges.

MOTIVATION The topology of the network induced by the neurons connectivity's in the Caenorhabditis elegans differs from most common random networks. The neurons positions of the C.elegans have been previously explained as being optimal to induce the required network wiring. We here propose a complementary explanation that the network wiring is the direct result of a local stochastic synapse formation process. RESULTS We show that a model based on the physical distance between neurons can explain the C.elegans neural network structure, specifically, we demonstrate that a simple model based on a geometrical synapse formation probability and the inhibition of short coherent cycles can explain the properties of the C.elegans' neural network. We suggest this model as an initial framework to discuss neural network generation and as a first step toward the development of models for more advanced creatures. In order to measure the circle frequency in the network, a novel graph-theory circle length measurement algorithm is proposed.

Collinear proximal flankers can facilitate the detection of a low-contrast target or generate false-alarm target detection in the absence of a target. Although these effects are known to involve subthreshold neuronal interactions beyond the classical receptive field, the underlying neuronal mechanisms are not fully understood. Here, we used voltage-sensitive dye imaging that emphasizes subthreshold population activity, at high spatial and temporal resolution and imaged the visual cortex of fixating monkeys while they were presented with a low-contrast Gabor target, embedded within collinear or orthogonal flankers. We found that neuronal activity at the target site in area primary visual cortex increased and response latency decreased due to spatial spread of activation from the flankers' site. This increased activity was smaller than expected by a linear summation. The presentation of flankers alone induced strong spatial filling-in at the target site. Importantly, the increased neuronal activity at the target site was synchronized over time, both locally and with neuronal population at the flanker's site. This onset synchronization was higher for collinear than for orthogonal flankers. We further show that synchrony is a superior code over amplitude, for discriminating collinear from orthogonal pattern. These results suggest that population synchrony can serve as a code to discriminate contextual effects.

The generation mechanisms of real world networks have been described using multiple models. The mathematical features of these models are usually extrapolated from statistical properties of a snapshot of these networks. We here propose an alternative method based on direct measurement of a sequence of consecutive snapshots to uncover the dynamics underlying real world generation. We assume that the probability of adding a node or an edge depends only on local features surrounding the newly added node/edge, and directly measure the contribution of these features to the node/edge addition probability. These measurements are performed using newly defined N-node local structures. Each N-node local structure represents the configuration of edges surrounding a newly added edge. The N-node local structure measurements reproduce for some networks the now classical addition of edges between high degree node mechanisms. It also provides quantitative estimates of more complex mechanisms driving other networks’ evolution, such as the effect of common first and second neighbors. This new methodology reveals the relative importance of different generation mechanisms. We show, for example, that the main mechanism driving hyperlink addition between two websites is the existence of a third website linking to both the source and the target of the new hyperlink.

Network motifs are small connected sub-graphs occurring at significantly higher frequencies in a given graph compared with random graphs of similar degree distribution. Recently, network motifs have attracted attention as a tool to study networks microscopic details. The commonly used algorithm for counting small-scale motifs is the one developed by Milo et al. This algorithm is extremely costly in CPU time and actually cannot work on large networks, consisting of more than 100,000 edges on current CPUs.We here present a new optimal algorithm, based on network decomposition for counting K-size network motifs with constant memory costs and a CPU cost linear with the number of counted motifs. Our algorithm performs better than previous full enumeration algorithms in terms of running time. Moreover, it uses a constant amount of memory. It also outperforms sampling algorithms. Our algorithm permits the counting of three and four motif for large networks that consists of more than 500,000 nodes and 5,000,000 links. For large networks, it performs more than a thousand times faster than current algorithms. (c) 2007 Elsevier B.V. All rights reserved.

The rapid accumulation of knowledge and the recent emergence of new dynamic and practically unmoderated information repositories have rendered the classical concept of the hierarchal knowledge structure irrelevant and impossible to impose manually. This led to modern methods of data location, such as browsing or searching, which conceal the underlying information structure. We here propose methods designed to automatically construct a hierarchy from a network of related terms. We apply these methods to Wikipedia and compare the hierarchy obtained from the article network to the complementary acyclic category layer of the Wikipedia and show an excellent fit. We verify our methods in two networks with no a priori hierarchy (the E. Coli genetic regulatory network and the C. Elegans neural network) and a network of function libraries of modern computer operating systems that are intrinsically hierarchical and reproduce a known functional order.