Identifying Influential Nodes in Large-Scale Directed Networks: The Role of Clustering

Identifying influential nodes in very large-scale directed networks is a big challenge relevant to disparate applications, such as accelerating information propagation, controlling rumors and diseases, designing search engines, and understanding hierarchical organization of social and biological networks. Known methods range from node centralities, such as degree, closeness and betweenness, to diffusion-based processes, like PageRank and LeaderRank. Some of these methods already take into account the influences of a node’s neighbors but do not directly make use of the interactions among it’s neighbors. Local clustering is known to have negative impacts on the information spreading. We further show empirically that it also plays a negative role in generating local connections. Inspired by these facts, we propose a local ranking algorithm named ClusterRank, which takes into account not only the number of neighbors and the neighbors’ influences, but also the clustering coefficient. Subject to the susceptible-infected-recovered (SIR) spreading model with constant infectivity, experimental results on two directed networks, a social network extracted from delicious.com and a large-scale short-message communication network, demonstrate that the ClusterRank outperforms some benchmark algorithms such as PageRank and LeaderRank. Furthermore, ClusterRank can also be applied to undirected networks where the superiority of ClusterRank is significant compared with degree centrality and k-core decomposition. In addition, ClusterRank, only making use of local information, is much more efficient than global methods: It takes only 191 seconds for a network with about nodes, more than 15 times faster than PageRank.     

On Nakhleh's Metric for Reduced Phylogenetic Networks

We prove that Nakhleh's metric for reduced phylogenetic networks is also a metric on the classes of tree-child phylogenetic networks, semibinary tree-sibling time consistent phylogenetic networks, and multilabeled phylogenetic trees. We also prove that it separates distinguishable phylogenetic networks. In this way, it becomes the strongest dissimilarity measure for phylogenetic networks available so far. Furthermore, we propose a generalization of that metric that separates arbitrary phylogenetic networks.     

A Bio-Inspired Methodology of Identifying Influential Nodes in Complex Networks

How to identify influential nodes is a key issue in complex networks. The degree centrality is simple, but is incapable to reflect the global characteristics of networks. Betweenness centrality and closeness centrality do not consider the location of nodes in the networks, and semi-local centrality, leaderRank and pageRank approaches can be only applied in unweighted networks. In this paper, a bio-inspired centrality measure model is proposed, which combines the Physarum centrality with the K-shell index obtained by K-shell decomposition analysis, to identify influential nodes in weighted networks. Then, we use the Susceptible-Infected (SI) model to evaluate the performance. Examples and applications are given to demonstrate the adaptivity and efficiency of the proposed method. In addition, the results are compared with existing methods.     

A Null Model for Pearson Coexpression Networks

Gene coexpression networks inferred by correlation from high-throughput profiling such as microarray data represent simple but effective structures for discovering and interpreting linear gene relationships. In recent years, several approaches have been proposed to tackle the problem of deciding when the resulting correlation values are statistically significant. This is most crucial when the number of samples is small, yielding a non-negligible chance that even high correlation values are due to random effects. Here we introduce a novel hard thresholding solution based on the assumption that a coexpression network inferred by randomly generated data is expected to be empty. The threshold is theoretically derived by means of an analytic approach and, as a deterministic independent null model, it depends only on the dimensions of the starting data matrix, with assumptions on the skewness of the data distribution compatible with the structure of gene expression levels data. We show, on synthetic and array datasets, that the proposed threshold is effective in eliminating all false positive links, with an offsetting cost in terms of false negative detected edges.     

Going the Distance for Protein Function Prediction: A New Distance Metric for Protein Interaction Networks

In protein-protein interaction (PPI) networks, functional similarity is often inferred based on the function of directly interacting proteins, or more generally, some notion of interaction network proximity among proteins in a local neighborhood. Prior methods typically measure proximity as the shortest-path distance in the network, but this has only a limited ability to capture fine-grained neighborhood distinctions, because most proteins are close to each other, and there are many ties in proximity. We introduce diffusion state distance (DSD), a new metric based on a graph diffusion property, designed to capture finer-grained distinctions in proximity for transfer of functional annotation in PPI networks. We present a tool that, when input a PPI network, will output the DSD distances between every pair of proteins. We show that replacing the shortest-path metric by DSD improves the performance of classical function prediction methods across the board.     

Identification of Important Nodes in Directed Biological Networks: A Network Motif Approach

Identification of important nodes in complex networks has attracted an increasing attention over the last decade. Various measures have been proposed to characterize the importance of nodes in complex networks, such as the degree, betweenness and PageRank. Different measures consider different aspects of complex networks. Although there are numerous results reported on undirected complex networks, few results have been reported on directed biological networks. Based on network motifs and principal component analysis (PCA), this paper aims at introducing a new measure to characterize node importance in directed biological networks. Investigations on five real-world biological networks indicate that the proposed method can robustly identify actually important nodes in different networks, such as finding command interneurons, global regulators and non-hub but evolutionary conserved actually important nodes in biological networks. Receiver Operating Characteristic (ROC) curves for the five networks indicate remarkable prediction accuracy of the proposed measure. The proposed index provides an alternative complex network metric. Potential implications of the related investigations include identifying network control and regulation targets, biological networks modeling and analysis, as well as networked medicine.     

Metrics for Phylogenetic Networks I: Generalizations of the Robinson-Foulds Metric

The assessment of phylogenetic network reconstruction methods requires the ability to compare phylogenetic networks. This is the first in a series of papers devoted to the analysis and comparison of metrics for tree-child time consistent phylogenetic networks on the same set of taxa. In this paper, we study three metrics that have already been introduced in the literature: the Robinson-Foulds distance, the tripartitions distance and the $mu$-distance. They generalize to networks the classical Robinson-Foulds or partition distance for phylogenetic trees. We analyze the behavior of these metrics by studying their least and largest values and when they achieve them. As a by-product of this study, we obtain tight bounds on the size of a tree-child time consistent phylogenetic network.     

A Universal Model of Commuting Networks

We show that a recently proposed model generates accurate commuting networks on 80 case studies from different regions of the world (Europe and United-States) at different scales (e.g. municipalities, counties, regions). The model takes as input the number of commuters coming in and out of each geographic unit and generates the matrix of commuting flows between the units. The single parameter of the model follows a universal law that depends only on the scale of the geographic units. We show that our model significantly outperforms two other approaches proposing a universal commuting model [1], [2], particularly when the geographic units are small (e.g. municipalities).     

A Framework of Algorithms: Computing the Bias and Prestige of Nodes in Trust Networks

A trust network is a social network in which edges represent the trust relationship between two nodes in the network. In a trust network, a fundamental question is how to assess and compute the bias and prestige of the nodes, where the bias of a node measures the trustworthiness of a node and the prestige of a node measures the importance of the node. The larger bias of a node implies the lower trustworthiness of the node, and the larger prestige of a node implies the higher importance of the node. In this paper, we define a vector-valued contractive function to characterize the bias vector which results in a rich family of bias measurements, and we propose a framework of algorithms for computing the bias and prestige of nodes in trust networks. Based on our framework, we develop four algorithms that can calculate the bias and prestige of nodes effectively and robustly. The time and space complexities of all our algorithms are linear with respect to the size of the graph, thus our algorithms are scalable to handle large datasets. We evaluate our algorithms using five real datasets. The experimental results demonstrate the effectiveness, robustness, and scalability of our algorithms.     

Controllability in Cancer Metabolic Networks According to Drug Targets as Driver Nodes

Networks are employed to represent many nonlinear complex systems in the real world. The topological aspects and relationships between the structure and function of biological networks have been widely studied in the past few decades. However dynamic and control features of complex networks have not been widely researched, in comparison to topological network features. In this study, we explore the relationship between network controllability, topological parameters, and network medicine (metabolic drug targets). Considering the assumption that targets of approved anticancer metabolic drugs are driver nodes (which control cancer metabolic networks), we have applied topological analysis to genome-scale metabolic models of 15 normal and corresponding cancer cell types. The results show that besides primary network parameters, more complex network metrics such as motifs and clusters may also be appropriate for controlling the systems providing the controllability relationship between topological parameters and drug targets. Consequently, this study reveals the possibilities of following a set of driver nodes in network clusters instead of considering them individually according to their centralities. This outcome suggests considering distributed control systems instead of nodal control for cancer metabolic networks, leading to a new strategy in the field of network medicine.     

A Model for Improving the Learning Curves of Artificial Neural Networks

In this article, the performance of a hybrid artificial neural network (i.e. scale-free and small-world) was analyzed and its learning curve compared to three other topologies: random, scale-free and small-world, as well as to the chemotaxis neural network of the nematode Caenorhabditis Elegans. One hundred equivalent networks (same number of vertices and average degree) for each topology were generated and each was trained for one thousand epochs. After comparing the mean learning curves of each network topology with the C. elegans neural network, we found that the networks that exhibited preferential attachment exhibited the best learning curves.     

Model requirements for Biobank Software Systems

Biobanks are essential tools in diagnostics and therapeutics research and development related to personalized medicine. Several international recommendations, standards and guidelines exist that discuss the legal, ethical, technological, and management requirements of biobanks. Today's biobanks are much more than just collections of biospecimens. They also store a huge amount of data related to biological samples which can be either clinical data or data coming from biochemical experiments. A well-designed biobank software system also provides the possibility of finding associations between stored elements. Modern research biobanks are able to manage multicenter sample collections while fulfilling all requirements of data protection and security. While developing several biobanks and analyzing the data stored in them, our research group recognized the need for a well-organized, easy-to-check requirements guideline that can be used to develop biobank software systems. International best practices along with relevant ICT standards were integrated into a comprehensive guideline: The Model Requirements for the Management of Biological Repositories (BioReq), which covers the full range of activities related to biobank development. The guideline is freely available on the Internet for the research community. AVAILABILITY: The database is available for free at http://bioreq.astridbio.com/bioreq_v2.0.pdf.     

A Discrete Velocity Kinetic Model with Food Metric: Chemotaxis Traveling Waves

We introduce a mesoscopic scale chemotaxis model for traveling wave phenomena which is induced by food metric. The organisms of this simplified kinetic model have two discrete velocity modes, \(\pm s\) and a constant tumbling rate. The main feature of the model is that the speed of organisms is constant \(s\,{>}\,0\) with respect to the food metric, not the Euclidean metric. The uniqueness and the existence of the traveling wave solution of the model are obtained. Unlike the classical logarithmic model case there exist traveling waves under super-linear consumption rates and infinite population pulse-type traveling waves are obtained. Numerical simulations are also provided.     

Optimized Null Model for Protein Structure Networks

Much attention has recently been given to the statistical significance of topological features observed in biological networks. Here, we consider residue interaction graphs (RIGs) as network representations of protein structures with residues as nodes and inter-residue interactions as edges. Degree-preserving randomized models have been widely used for this purpose in biomolecular networks. However, such a single summary statistic of a network may not be detailed enough to capture the complex topological characteristics of protein structures and their network counterparts. Here, we investigate a variety of topological properties of RIGs to find a well fitting network null model for them. The RIGs are derived from a structurally diverse protein data set at various distance cut-offs and for different groups of interacting atoms. We compare the network structure of RIGs to several random graph models. We show that 3-dimensional geometric random graphs, that model spatial relationships between objects, provide the best fit to RIGs. We investigate the relationship between the strength of the fit and various protein structural features. We show that the fit depends on protein size, structural class, and thermostability, but not on quaternary structure. We apply our model to the identification of significantly over-represented structural building blocks, i.e., network motifs, in protein structure networks. As expected, choosing geometric graphs as a null model results in the most specific identification of motifs. Our geometric random graph model may facilitate further graph-based studies of protein conformation space and have important implications for protein structure comparison and prediction. The choice of a well-fitting null model is crucial for finding structural motifs that play an important role in protein folding, stability and function. To our knowledge, this is the first study that addresses the challenge of finding an optimized null model for RIGs, by comparing various RIG definitions against a series of network models.     

ModuleRole: A Tool for Modulization,Role Determination and Visualization in Protein-Protein Interaction Networks

Rapidly increasing amounts of (physical and genetic) protein-protein interaction (PPI) data are produced by various high-throughput techniques, and interpretation of these data remains a major challenge. In order to gain insight into the organization and structure of the resultant large complex networks formed by interacting molecules, using simulated annealing, a method based on the node connectivity, we developed ModuleRole, a user-friendly web server tool which finds modules in PPI network and defines the roles for every node, and produces files for visualization in Cytoscape and Pajek. For given proteins, it analyzes the PPI network from BioGRID database, finds and visualizes the modules these proteins form, and then defines the role every node plays in this network, based on two topological parameters Participation Coefficient and Z-score. This is the first program which provides interactive and very friendly interface for biologists to find and visualize modules and roles of proteins in PPI network. It can be tested online at the website http://www.bioinfo.org/modulerole/index.php, which is free and open to all users and there is no login requirement, with demo data provided by “User Guide” in the menu Help. Non-server application of this program is considered for high-throughput data with more than 200 nodes or user’s own interaction datasets. Users are able to bookmark the web link to the result page and access at a later time. As an interactive and highly customizable application, ModuleRole requires no expert knowledge in graph theory on the user side and can be used in both Linux and Windows system, thus a very useful tool for biologist to analyze and visualize PPI networks from databases such as BioGRID.

Availability

ModuleRole is implemented in Java and C, and is freely available at http://www.bioinfo.org/modulerole/index.php. Supplementary information (user guide, demo data) is also available at this website. API for ModuleRole used for this program can be obtained upon request.     

Informal Exchange Networks in Formal Systems: A Theoretical Model

Studies of the informal economy in the Third World have evolved toward defining the informal sector in relationship to the state. This article analyzes some activities that escape the control of the state, with special attention to centrally planned economies. Informal exchanges include bureaucratic favors (connections), clientelism, different forms of corruption, and the parallel system of production and marketing. I show that economic laws are not sufficient to understand the logic of these economies.     

The LUX Score: A Metric for Lipidome Homology

A lipidome is the set of lipids in a given organism, cell or cell compartment and this set reflects the organism’s synthetic pathways and interactions with its environment. Recently, lipidomes of biological model organisms and cell lines were published and the number of functional studies of lipids is increasing. In this study we propose a homology metric that can quantify systematic differences in the composition of a lipidome. Algorithms were developed to 1. consistently convert lipids structure into SMILES, 2. determine structural similarity between molecular species and 3. describe a lipidome in a chemical space model. We tested lipid structure conversion and structure similarity metrics, in detail, using sets of isomeric ceramide molecules and chemically related phosphatidylinositols. Template-based SMILES showed the best properties for representing lipid-specific structural diversity. We also show that sequence analysis algorithms are best suited to calculate distances between such template-based SMILES and we adjudged the Levenshtein distance as best choice for quantifying structural changes. When all lipid molecules of the LIPIDMAPS structure database were mapped in chemical space, they automatically formed clusters corresponding to conventional chemical families. Accordingly, we mapped a pair of lipidomes into the same chemical space and determined the degree of overlap by calculating the Hausdorff distance. We named this metric the ‘Lipidome jUXtaposition (LUX) score’. First, we tested this approach for estimating the lipidome similarity on four yeast strains with known genetic alteration in fatty acid synthesis. We show that the LUX score reflects the genetic relationship and growth temperature better than conventional methods although the score is based solely on lipid structures. Next, we applied this metric to high-throughput data of larval tissue lipidomes of Drosophila. This showed that the LUX score is sufficient to cluster tissues and determine the impact of nutritional changes in an unbiased manner, despite the limited information on the underlying structural diversity of each lipidome. This study is the first effort to define a lipidome homology metric based on structures that will enrich functional association of lipids in a similar manner to measures used in genetics. Finally, we discuss the significance of the LUX score to perform comparative lipidome studies across species borders.     

Link Prediction in Weighted Networks: A Weighted Mutual Information Model

The link-prediction problem is an open issue in data mining and knowledge discovery, which attracts researchers from disparate scientific communities. A wealth of methods have been proposed to deal with this problem. Among these approaches, most are applied in unweighted networks, with only a few taking the weights of links into consideration. In this paper, we present a weighted model for undirected and weighted networks based on the mutual information of local network structures, where link weights are applied to further enhance the distinguishable extent of candidate links. Empirical experiments are conducted on four weighted networks, and results show that the proposed method can provide more accurate predictions than not only traditional unweighted indices but also typical weighted indices. Furthermore, some in-depth discussions on the effects of weak ties in link prediction as well as the potential to predict link weights are also given. This work may shed light on the design of algorithms for link prediction in weighted networks.