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PubMed2005

A graph spectral analysis of the structural similarity network of protein chains.

We present a simple method for the analysis of large networks based on their graph spectral properties. One of the advantages of this method is that it uses a single numerical computation to identify subclusters in a connected graph, which can significantly simplify the complexity involved in analyzing large graphs. This is illustrated using a network of protein chains constructed on the basis of their structural similarities. The large-scale network properties and the cluster and subcluster organization of the protein chain network are presented. We summarize the results of structural and functional analyses of the nodes present in these clusters and elucidate the implications of structural similarity in the protein chain universe.

Cluster Analysis↗
PubMedDate not supplied

IPSEP-COLA: an incremental procedure for separation constraint layout of graphs.

We extend the popular force-directed approach to network (or graph) layout to allow separation constraints, which enforce a minimum horizontal or vertical separation between selected pairs of nodes. This simple class of linear constraints is expressive enough to satisfy a wide variety of application-specific layout requirements, including: layout of directed graphs to better show flow; layout with non-overlapping node labels; and layout of graphs with grouped nodes (called clusters). In the stress majorization force-directed layout process, separation constraints can be treated as a quadratic programming problem. We give an incremental algorithm based on gradient projection for efficiently solving this problem. The algorithm is considerably faster than using generic constraint optimization techniques and is comparable in speed to unconstrained stress majorization. We demonstrate the utility of our technique with sample data from a number of practical applications including gene-activation networks, terrorist networks and visualization of high-dimensional data.

Journal Article↗
PubMed2003

Modeling proteome networks with range-dependent graphs.

In this paper we consider the problem of characterizing and modeling large-scale protein-protein association networks using a class of range-dependent graphs which possess appropriate small world properties. These graphs may be employed in representing given association network using a maximum likelihood approach. This in turn annotates every observed association with its 'range', representing the tendency for such an association to be transitive. The application of a very rapidly developing field of graph theory to the emerging field of proetemics is novel and allows for a many-to-many relationship between individual proteins and groupings of proteins, which in turn may correspond to distinct functional behavior.

Models, Biological↗
PubMed2006

Low-order conditional independence graphs for inferring genetic networks.

As a powerful tool for analyzing full conditional (in-)dependencies between random variables, graphical models have become increasingly popular to infer genetic networks based on gene expression data. However, full (unconstrained) conditional relationships between random variables can be only estimated accurately if the number of observations is relatively large in comparison to the number of variables, which is usually not fulfilled for high-throughput genomic data. Recently, simplified graphical modeling approaches have been proposed to determine dependencies between gene expression profiles. For sparse graphical models such as genetic networks, it is assumed that the zero- and first-order conditional independencies still reflect reasonably well the full conditional independence structure between variables. Moreover, low-order conditional independencies have the advantage that they can be accurately estimated even when having only a small number of observations. Therefore, using only zero- and first-order conditional dependencies to infer the complete graphical model can be very useful. Here, we analyze the statistical and probabilistic properties of these low-order conditional independence graphs (called 0-1 graphs). We find that for faithful graphical models, the 0-1 graph contains at least all edges of the full conditional independence graph (concentration graph). For simple structures such as Markov trees, the 0-1 graph even coincides with the concentration graph. Furthermore, we present some asymptotic results and we demonstrate in a simulation study that despite their simplicity, 0-1 graphs are generally good estimators of sparse graphical models. Finally, the biological relevance of some applications is summarized.

Algorithms↗
PubMed2006

A methodology for the structural and functional analysis of signaling and regulatory networks.

BACKGROUND: Structural analysis of cellular interaction networks contributes to a deeper understanding of network-wide interdependencies, causal relationships, and basic functional capabilities. While the structural analysis of metabolic networks is a well-established field, similar methodologies have been scarcely developed and applied to signaling and regulatory networks. RESULTS: We propose formalisms and methods, relying on adapted and partially newly introduced approaches, which facilitate a structural analysis of signaling and regulatory networks with focus on functional aspects. We use two different formalisms to represent and analyze interaction networks: interaction graphs and (logical) interaction hypergraphs. We show that, in interaction graphs, the determination of feedback cycles and of all the signaling paths between any pair of species is equivalent to the computation of elementary modes known from metabolic networks. Knowledge on the set of signaling paths and feedback loops facilitates the computation of intervention strategies and the classification of compounds into activators, inhibitors, ambivalent factors, and non-affecting factors with respect to a certain species. In some cases, qualitative effects induced by perturbations can be unambiguously predicted from the network scheme. Interaction graphs however, are not able to capture AND relationships which do frequently occur in interaction networks. The consequent logical concatenation of all the arcs pointing into a species leads to Boolean networks. For a Boolean representation of cellular interaction networks we propose a formalism based on logical (or signed) interaction hypergraphs, which facilitates in particular a logical steady state analysis (LSSA). LSSA enables studies on the logical processing of signals and the identification of optimal intervention points (targets) in cellular networks. LSSA also reveals network regions whose parametrization and initial states are crucial for the dynamic behavior. We have implemented these methods in our software tool CellNetAnalyzer (successor of FluxAnalyzer) and illustrate their applicability using a logical model of T-Cell receptor signaling providing non-intuitive results regarding feedback loops, essential elements, and (logical) signal processing upon different stimuli. CONCLUSION: The methods and formalisms we propose herein are another step towards the comprehensive functional analysis of cellular interaction networks. Their potential, shown on a realistic T-cell signaling model, makes them a promising tool.

Animals↗
PubMedDate not supplied

Motif search in graphs: application to metabolic networks.

The classic view of metabolism as a collection of metabolic pathways is being questioned with the currently available possibility of studying whole networks. Novel ways of decomposing the network into modules and motifs that could be considered as the building blocks of a network are being suggested. In this work, we introduce a new definition of motif in the context of metabolic networks. Unlike in previous works on (other) biochemical networks, this definition is not based only on topological features. We propose instead to use an alternative definition based on the functional nature of the components that form the motif, which we call a reaction motif. After introducing a formal framework motivated by biological considerations, we present complexity results on the problem of searching for all occurrences of a reaction motif in a network and introduce an algorithm that is fast in practice in most situations. We then show an initial application to the study of pathway evolution. Finally, we give some general features of the observed number of occurrences in order to highlight some structural features of metabolic networks.

Algorithms↗
PubMed2006

An experimental study of the coloring problem on human subject networks.

Theoretical work suggests that structural properties of naturally occurring networks are important in shaping behavior and dynamics. However, the relationships between structure and behavior are difficult to establish through empirical studies, because the networks in such studies are typically fixed. We studied networks of human subjects attempting to solve the graph or network coloring problem, which models settings in which it is desirable to distinguish one's behavior from that of one's network neighbors. Networks generated by preferential attachment made solving the coloring problem more difficult than did networks based on cyclical structures, and "small worlds" networks were easier still. We also showed that providing more information can have opposite effects on performance, depending on network structure.

Game Theory↗
PubMed2000

Network robustness and fragility: percolation on random graphs.

Recent work on the Internet, social networks, and the power grid has addressed the resilience of these networks to either random or targeted deletion of network nodes or links. Such deletions include, for example, the failure of Internet routers or power transmission lines. Percolation models on random graphs provide a simple representation of this process but have typically been limited to graphs with Poisson degree distribution at their vertices. Such graphs are quite unlike real-world networks, which often possess power-law or other highly skewed degree distributions. In this paper we study percolation on graphs with completely general degree distribution, giving exact solutions for a variety of cases, including site percolation, bond percolation, and models in which occupation probabilities depend on vertex degree. We discuss the application of our theory to the understanding of network resilience.

Algorithms↗
PubMed2005

Graph theoretic modeling of large-scale semantic networks.

During the past several years, social network analysis methods have been used to model many complex real-world phenomena, including social networks, transportation networks, and the Internet. Graph theoretic methods, based on an elegant representation of entities and relationships, have been used in computational biology to study biological networks; however they have not yet been adopted widely by the greater informatics community. The graphs produced are generally large, sparse, and complex, and share common global topological properties. In this review of research (1998-2005) on large-scale semantic networks, we used a tailored search strategy to identify articles involving both a graph theoretic perspective and semantic information. Thirty-one relevant articles were retrieved. The majority (28, 90.3%) involved an investigation of a real-world network. These included corpora, thesauri, dictionaries, large computer programs, biological neuronal networks, word association networks, and files on the Internet. Twenty-two of the 28 (78.6%) involved a graph comprised of words or phrases. Fifteen of the 28 (53.6%) mentioned evidence of small-world characteristics in the network investigated. Eleven (39.3%) reported a scale-free topology, which tends to have a similar appearance when examined at varying scales. The results of this review indicate that networks generated from natural language have topological properties common to other natural phenomena. It has not yet been determined whether artificial human-curated terminology systems in biomedicine share these properties. Large network analysis methods have potential application in a variety of areas of informatics, such as in development of controlled vocabularies and for characterizing a given domain.

Algorithms↗
PubMed2004

Prediction of splice sites with dependency graphs and their expanded bayesian networks.

MOTIVATION: Owing to the complete sequencing of human and many other genomes, huge amounts of DNA sequence data have been accumulated. In bioinformatics, an important issue is how to predict the complete structure of genes from the genomic DNA sequence, especially the human genome. A crucial part in the gene structure prediction is to determine the precise exon-intron boundaries, i.e. the splice sites, in the coding region. RESULTS: We have developed a dependency graph model to fully capture the intrinsic interdependency between base positions in a splice site. The establishment of dependency between two position is based on a chi2-test from known sample data. To facilitate statistical inference, we have expanded the dependency graph (which is usually a graph with cycles that make probabilistic reasoning very difficult, if not impossible) into a Bayesian network (which is a directed acyclic graph that facilitates statistical reasoning). When compared with the existing models such as weight matrix model, weight array model, maximal dependence decomposition, Cai et al.'s tree model as well as the less-studied second-order and third-order Markov chain models, the expanded Bayesian networks from our dependency graph models perform the best in nearly all the cases studied. AVAILABILITY: Software (a program called DGSplicer) and datasets used are available at http://csrl.ee.nthu.edu.tw/bioinf/ CONTACT: cclu@ee.nthu.edu.tw.

Bayes Theorem↗
PubMed1996

A simple model for the statistics of events in idiotypic networks.

A simple random graph model of idiotypic networks is introduced: this model allows (1) to evaluate the stability of the network dynamics' fixed points, and (2) to compute the statistics of events triggered in response to the arrival of new molecules (metadynamics) using a dynamic mean-field approximation based on the theory of branching processes. It is shown that (1) the network dynamics is unlikely to have many stable fixed points in a strict sense, but that (2) the reorganizations which the network undergoes owing to the metadynamics are always subcritical if plausible figures are injected into the model. In other words the distance between successive (unstable or weakly stable) fixed points is relatively small, so that the overall behavior is stable.

Animals↗
PubMed2006

Recursive processing of cyclic graphs.

Recursive neural networks are a powerful tool for processing structured data. According to the recursive learning paradigm, the input information consists of directed positional acyclic graphs (DPAGs). In fact, recursive networks are fed following the partial order defined by the links of the graph. Unfortunately, the hypothesis of processing DPAGs is sometimes too restrictive, being the nature of some real-world problems intrinsically cyclic. In this paper, a methodology is proposed, which allows us to process any cyclic directed graph. Therefore, the computational power of recursive networks is definitely established, also clarifying the underlying limitations of the model.

Journal Article↗
PubMed2005

A grid layout algorithm for automatic drawing of biochemical networks.

MOTIVATION: Visualization is indispensable in the research of complex biochemical networks. Available graph layout algorithms are not adequate for satisfactorily drawing such networks. New methods are required to visualize automatically the topological architectures and facilitate the understanding of the functions of the networks. RESULTS: We propose a novel layout algorithm to draw complex biochemical networks. A network is modeled as a system of interacting nodes on squared grids. A discrete cost function between each node pair is designed based on the topological relation and the geometric positions of the two nodes. The layouts are produced by minimizing the total cost. We design a fast algorithm to minimize the discrete cost function, by which candidate layouts can be produced efficiently. A simulated annealing procedure is used to choose better candidates. Our algorithm demonstrates its ability to exhibit cluster structures clearly in relatively compact layout areas without any prior knowledge. We developed Windows software to implement the algorithm for CADLIVE. AVAILABILITY: All materials can be freely downloaded from http://kurata21.bio.kyutech.ac.jp/grid/grid_layout.htm; http://www.cadlive.jp/ SUPPLEMENTARY INFORMATION: http://kurata21.bio.kyutech.ac.jp/grid/grid_layout.htm; http://www.cadlive.jp/

Algorithms↗
PubMed2006

Scale-free networks emerging from weighted random graphs.

We study Erdös-Rényi random graphs with random weights associated with each link. We generate a "supernode network" by merging all nodes connected by links having weights below the percolation threshold (percolation clusters) into a single node. We show that this network is scale-free, i.e., the degree distribution is P(k) approximately k(-lambda) with lambda=2.5. Our results imply that the minimum spanning tree in random graphs is composed of percolation clusters, which are interconnected by a set of links that create a scale-free tree with lambda=2.5. We suggest that optimization causes the percolation threshold to emerge spontaneously, thus creating naturally a scale-free supernode network. We discuss the possibility that this phenomenon is related to the evolution of several real world scale-free networks.

Journal Article↗
PubMed2005

Spectral measures of bipartivity in complex networks.

We introduce a quantitative measure of network bipartivity as a proportion of even to total number of closed walks in the network. Spectral graph theory is used to quantify how close to bipartite a network is and the extent to which individual nodes and edges contribute to the global network bipartivity. It is shown that the bipartivity characterizes the network structure and can be related to the efficiency of semantic or communication networks, trophic interactions in food webs, construction principles in metabolic networks, or communities in social networks.

Journal Article↗
PubMed2026

GiGCN: a network-based framework for uncovering synthetic lethal and viable genetic interactions.

Genetic interactions (GIs) underpin the functional connectivity of genes and pathways, and are important for dissecting genotype-phenotype relationships and identifying therapeutic targets for diseases. However, the scale of the human genome restricts systematic experimental interrogation of GIs. Existing computational tools focus on predicting synthetic lethality (SL) and synthetic viability (SV), the two primary forms of GIs, yet their accuracy and biological interpretability are compromised by inadequate modeling of the molecular mechanisms behind positive and negative interactions, as well as the limitation of negative samples. To overcome these challenges, we developed Genetic Interaction Graph Convolutional Network (GiGCN), a signed network modeling framework for the joint identification of gene pairs with SL and SV. We built a high-confidence signed genetic network by integrating verified GIs, and non-interacting gene pairs, together with gene semantic similarity derived from biological processes. By leveraging disentangled subspace decomposition, this framework separately models distinct functional dimensions within gene networks, enabling robust representation of context-dependent regulatory relationships and accurate discrimination of SL and SV events. Benchmark experiments demonstrate that GiGCN outperforms state-of-the-art approaches (area under receiver operating-characteristic curve: 0.978, and area under precision-recall curve: 0.944). Further analyses reveal biologically meaningful insights, including known and novel SL interactions centered on the oncogene MYC Proto-Oncogene (MYC), as well as SV interactions linked to autophagy and mitophagy pathways. This study provides a robust and interpretable network-based strategy for systematically exploring GIs. The GiGCN framework not only improves the precision of SL and SV prediction, but also offers mechanistic insights into gene functional relationships, thereby supporting the discovery of actionable therapeutic targets for cancer and other human diseases.

Humans↗
PubMed2005

Complex networks emerging from fluctuating random graphs: analytic formula for the hidden variable distribution.

In analogy to superstatistics, which connects Boltzmann-Gibbs statistical mechanics to its generalizations through temperature fluctuations, complex networks are constructed from fluctuating Erdös-Rényi random graphs. Using a quantum-mechanical method, the exact analytic formula for the hidden variable distribution is presented which describes the nature of the fluctuations and generates a generic degree distribution through the Poisson transformation. As an example, a static scale-free network is discussed and the corresponding hidden variable distribution is found to decay as a power law and to diverge at the origin.

Algorithms↗
PubMed2025

A Graph Contrastive Learning Method for Enhancing Genome Recovery in Complex Microbial Communities.

Accurate genome binning is essential for resolving microbial community structure and functional potential from metagenomic data. However, existing approaches-primarily reliant on tetranucleotide frequency (TNF) and abundance profiles-often perform sub-optimally in the face of complex community compositions, low-abundance taxa, and long-read sequencing datasets. To address these limitations, we present MBGCCA, a novel metagenomic binning framework that synergistically integrates graph neural networks (GNNs), contrastive learning, and information-theoretic regularization to enhance binning accuracy, robustness, and biological coherence. MBGCCA operates in two stages: (1) multimodal information integration, where TNF and abundance profiles are fused via a deep neural network trained using a multi-view contrastive loss, and (2) self-supervised graph representation learning, which leverages assembly graph topology to refine contig embeddings. The contrastive learning objective follows the InfoMax principle by maximizing mutual information across augmented views and modalities, encouraging the model to extract globally consistent and high-information representations. By aligning perturbed graph views while preserving topological structure, MBGCCA effectively captures both global genomic characteristics and local contig relationships. Comprehensive evaluations using both synthetic and real-world datasets-including wastewater and soil microbiomes-demonstrate that MBGCCA consistently outperforms state-of-the-art binning methods, particularly in challenging scenarios marked by sparse data and high community complexity. These results highlight the value of entropy-aware, topology-preserving learning for advancing metagenomic genome reconstruction.

canonical correlation analysis↗