Illés J. Farkas

Uncovering the overlapping community structure of complex networks in nature and society

Many complex systems in nature and society can be described in terms of networks capturing the intricate web of connections among the units they are made of. A key question is how to interpret the global organization of such networks as the coexistence of their structural subunits (communities) associated with more highly interconnected parts. Identifying these a priori unknown building blocks (such as functionally related proteins, industrial sectors and groups of people) is crucial to the understanding of the structural and functional properties of networks. The existing deterministic methods used for large networks find separated communities, whereas most of the actual networks are made of highly overlapping cohesive groups of nodes. Here we introduce an approach to analysing the main statistical features of the interwoven sets of overlapping communities that makes a step towards uncovering the modular structure of complex systems. After defining a set of new characteristic quantities for the statistics of communities, we apply an efficient technique for exploring overlapping communities on a large scale. We find that overlaps are significant, and the distributions we introduce reveal universal features of networks. Our studies of collaboration, word-association and protein interaction graphs show that the web of communities has non-trivial correlations and specific scaling properties.

CFinder: locating cliques and overlapping modules in biological networks

UNLABELLED Most cellular tasks are performed not by individual proteins, but by groups of functionally associated proteins, often referred to as modules. In a protein association network modules appear as groups of densely interconnected nodes, also called communities or clusters. These modules often overlap with each other and form a network of their own, in which nodes (links) represent the modules (overlaps). We introduce CFinder, a fast program locating and visualizing overlapping, densely interconnected groups of nodes in undirected graphs, and allowing the user to easily navigate between the original graph and the web of these groups. We show that in gene (protein) association networks CFinder can be used to predict the function(s) of a single protein and to discover novel modules. CFinder is also very efficient for locating the cliques of large sparse graphs. AVAILABILITY CFinder (for Windows, Linux and Macintosh) and its manual can be downloaded from http://angel.elte.hu/clustering. SUPPLEMENTARY INFORMATION Supplementary data are available on Bioinformatics online.

Self-Organizing Pedestrian Movement

Although pedestrians have individual preferences, aims, and destinations, the dynamics of pedestrian crowds is surprisingly predictable. Pedestrians can move freely only at small pedestrian densities. Otherwise their motion is affected by repulsive interactions with other pedestrians, giving rise to self-organization phenomena. Examples of the resulting patterns of motion are separate lanes of uniform walking direction in crowds of oppositely moving pedestrians or oscillations of the passing direction at bottlenecks. If pedestrians leave footprints on deformable ground (for example, in green spaces such as public parks) this additionally causes attractive interactions which are mediated by modifications of their environment. In such cases, systems of pedestrian trails will evolve over time. The corresponding computer simulations are a valuable tool for developing optimized pedestrian facilities and way systems.

Spectra of "real-world" graphs: beyond the semicircle law.

Many natural and social systems develop complex networks that are usually modeled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semicircle law is known to describe the spectral densities of uncorrelated random graphs, much less is known about the spectra of real-world graphs, describing such complex systems as the Internet, metabolic pathways, networks of power stations, scientific collaborations, or movie actors, which are inherently correlated and usually very sparse. An important limitation in addressing the spectra of these systems is that the numerical determination of the spectra for systems with more than a few thousand nodes is prohibitively time and memory consuming. Making use of recent advances in algorithms for spectral characterization, here we develop methods to determine the eigenvalues of networks comparable in size to real systems, obtaining several surprising results on the spectra of adjacency matrices corresponding to models of real-world graphs. We find that when the number of links grows as the number of nodes, the spectral density of uncorrelated random matrices does not converge to the semicircle law. Furthermore, the spectra of real-world graphs have specific features, depending on the details of the corresponding models. In particular, scale-free graphs develop a trianglelike spectral density with a power-law tail, while small-world graphs have a complex spectral density consisting of several sharp peaks. These and further results indicate that the spectra of correlated graphs represent a practical tool for graph classification and can provide useful insight into the relevant structural properties of real networks.

Weighted network modules

The inclusion of link weights into the analysis of network properties allows a deeper insight into the (often overlapping) modular structure of real- world webs. We introduce a clustering algorithm clique percolation method with weights (CPMw) for weighted networks based on the concept of percolating k-cliques with high enough intensity. The algorithm allows overlaps between the modules. First, we give detailed analytical and numerical results about the critical point of weighted k-clique percolation on (weighted) Erdý os-Renyi graphs. Then, for a scientist collaboration web and a stock correlation graph we compute three-link weight correlations and with the CPMw the weighted modules. After reshuffling link weights in both networks and computing the same quantities for the randomized control graphs as well, we show that groups of three or more strong links prefer to cluster together in both original graphs.

Mexican Waves in an Excitable Medium

Mexican wave, or La Ola, first widely broadcasted during the 1986 World Cup held in Mexico, is a human wave moving along the stands of stadiums as one section of spectators stands up, arms lifting, then sits down as the next section does the same. Here we use variants of models originally developed for the description of excitable media to demonstrate that this collective human behaviour can be quantitatively interpreted by methods of statistical physics. Adequate modelling of reactions to triggering attempts provides a deeper insight into the mechanisms by which a crowd can be stimulated to execute a particular pattern of behaviour and represents a possible tool of control during events involving excited groups of people.The Mexican wave, or La Ola, which rose to fame during the 1986 World Cup in Mexico, surges through the rows of spectators in a stadium as those in one section leap to their feet with their arms up, and then sit down again as the next section rises to repeat the motion. To interpret and quantify this collective human behaviour, we have used a variant of models that were originally developed to describe excitable media such as cardiac tissue. Modelling the reaction of the crowd to attempts to trigger the wave reveals how this phenomenon is stimulated, and may prove useful in controlling events that involve groups of excited people.

Directed network modules

A search technique locating network modules, i.e. internally densely connected groups of nodes in directed networks is introduced by extending the clique percolation method originally proposed for undirected networks. After giving a suitable definition for directed modules we investigate their percolation transition in the Erdős–Renyi graph both analytically and numerically. We also analyse four real-world directed networks, including Googles own web-pages, an email network, a word association graph and the transcriptional regulatory network of the yeast Saccharomyces cerevisiae. The obtained directed modules are validated by additional information available for the nodes. We find that directed modules of real-world graphs inherently overlap and the investigated networks can be classified into two major groups in terms of the overlaps between the modules. Accordingly, in the word-association network and Googles web-pages, overlaps are likely to contain in-hubs, whereas the modules in the email and transcriptional regulatory network tend to overlap via out-hubs.

The topology of the transcription regulatory network in the yeast, Saccharomyces cerevisiae

A control device having a housing provided with a movable actuator and a rotatable selector shaft for positioning the actuator in relation to the rotational position of the shaft. An actuator driver is carried by the shaft and is operatively interconnected to the actuator to drive the same upon rotation of the driver by the shaft, the shaft and driver being axially movable relative to the actuator. The housing has a latching part cooperable with a latching part of the driver when the shaft is in a certain rotational and axial position relative to the housing whereby the shaft cannot be rotated relative to the housing until the shaft is axially moved from that certain axial position thereof to another axial position thereof to clear the latching part of the driver from the latching part of the housing and thereby unlock the selector shaft.

SignaLink 2 - a signaling pathway resource with multi-layered regulatory networks

BackgroundSignaling networks in eukaryotes are made up of upstream and downstream subnetworks. The upstream subnetwork contains the intertwined network of signaling pathways, while the downstream regulatory part contains transcription factors and their binding sites on the DNA as well as microRNAs and their mRNA targets. Currently, most signaling and regulatory databases contain only a subsection of this network, making comprehensive analyses highly time-consuming and dependent on specific data handling expertise. The need for detailed mapping of signaling systems is also supported by the fact that several drug development failures were caused by undiscovered cross-talk or regulatory effects of drug targets. We previously created a uniformly curated signaling pathway resource, SignaLink, to facilitate the analysis of pathway cross-talks. Here, we present SignaLink 2, which significantly extends the coverage and applications of its predecessor.DescriptionWe developed a novel concept to integrate and utilize different subsections (i.e., layers) of the signaling network. The multi-layered (onion-like) database structure is made up of signaling pathways, their pathway regulators (e.g., scaffold and endocytotic proteins) and modifier enzymes (e.g., phosphatases, ubiquitin ligases), as well as transcriptional and post-transcriptional regulators of all of these components. The user-friendly website allows the interactive exploration of how each signaling protein is regulated. The customizable download page enables the analysis of any user-specified part of the signaling network. Compared to other signaling resources, distinctive features of SignaLink 2 are the following: 1) it involves experimental data not only from humans but from two invertebrate model organisms, C. elegans and D. melanogaster; 2) combines manual curation with large-scale datasets; 3) provides confidence scores for each interaction; 4) operates a customizable download page with multiple file formats (e.g., BioPAX, Cytoscape, SBML). Non-profit users can access SignaLink 2 free of charge at http://SignaLink.org.ConclusionsWith SignaLink 2 as a single resource, users can effectively analyze signaling pathways, scaffold proteins, modifier enzymes, transcription factors and miRNAs that are important in the regulation of signaling processes. This integrated resource allows the systems-level examination of how cross-talks and signaling flow are regulated, as well as provide data for cross-species comparisons and drug discovery analyses.

Uniformly curated signaling pathways reveal tissue-specific cross-talks and support drug target discovery

MOTIVATION Signaling pathways control a large variety of cellular processes. However, currently, even within the same database signaling pathways are often curated at different levels of detail. This makes comparative and cross-talk analyses difficult. RESULTS We present SignaLink, a database containing eight major signaling pathways from Caenorhabditis elegans, Drosophila melanogaster and humans. Based on 170 review and approximately 800 research articles, we have compiled pathways with semi-automatic searches and uniform, well-documented curation rules. We found that in humans any two of the eight pathways can cross-talk. We quantified the possible tissue- and cancer-specific activity of cross-talks and found pathway-specific expression profiles. In addition, we identified 327 proteins relevant for drug target discovery. CONCLUSIONS We provide a novel resource for comparative and cross-talk analyses of signaling pathways. The identified multi-pathway and tissue-specific cross-talks contribute to the understanding of the signaling complexity in health and disease, and underscore its importance in network-based drug target selection. AVAILABILITY http://SignaLink.org.