Extracting Dense and Connected Subgraphs in Dual Networks by Network Alignment

The use of network based approaches to model and analyse large datasets is currently a growing research field. For instance in biology and medicine, networks are used to model interactions among biological molecules as well as relations among patients. Similarly, data coming from social networks can be trivially modelled by using graphs. More recently, the use of dual networks gained the attention of researchers. A dual network model uses a pair of graphs to model a scenario in which one of the two graphs is usually unweighted (a network representing physical associations among nodes) while the other one is edge-weighted (a network representing conceptual associations among nodes). In this paper we focus on the problem of finding the Densest Connected sub-graph (DCS) having the largest density in the conceptual network which is also connected in the physical network. The problem is relevant but also computationally hard, therefore the need for introducing of novel algorithms arises. We formalise the problem and then we map DCS into a graph alignment problem. Then we propose a possible solution. A set of experiments is also presented to support our approach

Optimal Network Alignment with Graphlet Degree Vectors

Important biological information is encoded in the topology of biological networks. Comparative analyses of biological networks are proving to be valuable, as they can lead to transfer of knowledge between species and give deeper insights into biological function, disease, and evolution. We introduce a new method that uses the Hungarian algorithm to produce optimal global alignment between two networks using any cost function. We design a cost function based solely on network topology and use it in our network alignment. Our method can be applied to any two networks, not just biological ones, since it is based only on network topology. We use our new method to align protein-protein interaction networks of two eukaryotic species and demonstrate that our alignment exposes large and topologically complex regions of network similarity. At the same time, our alignment is biologically valid, since many of the aligned protein pairs perform the same biological function. From the alignment, we predict function of yet unannotated proteins, many of which we validate in the literature. Also, we apply our method to find topological similarities between metabolic networks of different species and build phylogenetic trees based on our network alignment score. The phylogenetic trees obtained in this way bear a striking resemblance to the ones obtained by sequence alignments. Our method detects topologically similar regions in large networks that are statistically significant. It does this independent of protein sequence or any other information external to network topology

Parallel Exchange of Randomized SubGraphs for Optimization of Network Alignment: PERSONA

The aim of Network Alignment in Protein-Protein Interaction Networks is discovering functionally similar regions between compared organisms. One major compromise for solving a network alignment problem is the trade-off among multiple similarity objectives while applying an alignment strategy. An alignment may lose its biological relevance while favoring certain objectives upon others due to the actual relevance of unfavored objectives. One possible solution for solving this issue may be blending the stronger aspects of various alignment strategies until achieving mature solutions. This study proposes a parallel approach called PERSONA that allows aligners to share their partial solutions continuously while they progress. All these aligners pursue their particular heuristics as part of a particle swarm that searches for multi-objective solutions of the same alignment problem in a reactive actor environment. The actors use the stronger portion of a solution as a subgraph that they receive from leading or other actors and send their own stronger subgraphs back upon evaluation of those partial solutions. Moreover, the individual heuristics of each actor takes randomized parameter values at each cycle of parallel execution so that the problem search space can thoroughly be investigated. The results achieved with PERSONA are remarkably optimized and balanced for both topological and node similarity objectives

MuLaN: a MultiLayer Networks Alignment Algorithm

A Multilayer Network (MN) is a system consisting of several topological levels (i.e., layers) representing the interactions between the system's objects and the related interdependency. Therefore, it may be represented as a set of layers that can be assimilated to a set of networks of its own objects, by means inter-layer edges (or inter-edges) linking the nodes of different layers; for instance, a biological MN may allow modeling of inter and intra interactions among diseases, genes, and drugs, only using its own structure. The analysis of MNs may reveal hidden knowledge, as demonstrated by several algorithms for the analysis. Recently, there is a growing interest in comparing two MNs by revealing local regions of similarity, as a counterpart of Network Alignment algorithms (NA) for simple networks. However, classical algorithms for NA such as Local NA (LNA) cannot be applied on multilayer networks, since they are not able to deal with inter-layer edges. Therefore, there is the need for the introduction of novel algorithms. In this paper, we present MuLaN, an algorithm for the local alignment of multilayer networks. We first show as proof of concept the performances of MuLaN on a set of synthetic multilayer networks. Then, we used as a case study a real multilayer network in the biomedical domain. Our results show that MuLaN is able to build high-quality alignments and can extract knowledge about the aligned multilayer networks. MuLaN is available at https://github.com/pietrocinaglia/mulan

Integrative Analysis of Many Weighted Co-Expression Networks Using Tensor Computation

The rapid accumulation of biological networks poses new challenges and calls for powerful integrative analysis tools. Most existing methods capable of simultaneously analyzing a large number of networks were primarily designed for unweighted networks, and cannot easily be extended to weighted networks. However, it is known that transforming weighted into unweighted networks by dichotomizing the edges of weighted networks with a threshold generally leads to information loss. We have developed a novel, tensor-based computational framework for mining recurrent heavy subgraphs in a large set of massive weighted networks. Specifically, we formulate the recurrent heavy subgraph identification problem as a heavy 3D subtensor discovery problem with sparse constraints. We describe an effective approach to solving this problem by designing a multi-stage, convex relaxation protocol, and a non-uniform edge sampling technique. We applied our method to 130 co-expression networks, and identified 11,394 recurrent heavy subgraphs, grouped into 2,810 families. We demonstrated that the identified subgraphs represent meaningful biological modules by validating against a large set of compiled biological knowledge bases. We also showed that the likelihood for a heavy subgraph to be meaningful increases significantly with its recurrence in multiple networks, highlighting the importance of the integrative approach to biological network analysis. Moreover, our approach based on weighted graphs detects many patterns that would be overlooked using unweighted graphs. In addition, we identified a large number of modules that occur predominately under specific phenotypes. This analysis resulted in a genome-wide mapping of gene network modules onto the phenome. Finally, by comparing module activities across many datasets, we discovered high-order dynamic cooperativeness in protein complex networks and transcriptional regulatory networks