Network theory

About: Network theory is a research topic. Over the lifetime, 2257 publications have been published within this topic receiving 109864 citations.

When metabolism meets topology: Reconciling metabolite and reaction networks.

Abstract: The search for a systems-level picture of metabolism as a web of molecular interactions provides a paradigmatic example of how the methods used to characterize a system can bias the interpretation of its functional meaning Metabolic maps have been analyzed using novel techniques from network theory, revealing some non-trivial, functionally relevant properties These include a small-world structure and hierarchical modularity However, as discussed here, some of these properties might actually result from an inappropriate way of defining network interactions Starting from the so-called bipartite organization of metabolism, where the two meaningful subsets (reactions and metabolites) are considered, most current works use only one of the subsets by means of so-called graph projections Unfortunately, projected graphs often ignore relevant biological and chemical constraints, thus leading to statistical artifacts Some of these drawbacks and alternative approaches need to be properly addressed

Scalable Online Betweenness Centrality in Evolving Graphs

Abstract: Betweenness centrality is a classic measure that quantifies the importance of a graph element (vertex or edge) according to the fraction of shortest paths passing through it. This measure is notoriously expensive to compute, and the best known algorithm runs in $\mathcal {O}(nm)$ time. The problems of efficiency and scalability are exacerbated in a dynamic setting, where the input is an evolving graph seen edge by edge, and the goal is to keep the betweenness centrality up to date. In this paper, we propose the first truly scalable algorithm for online computation of betweenness centrality of both vertices and edges in an evolving graph where new edges are added and existing edges are removed. Our algorithm is carefully engineered with out-of-core techniques and tailored for modern parallel stream processing engines that run on clusters of shared-nothing commodity hardware. Hence, it is amenable to real-world deployment. We experiment on graphs that are two orders of magnitude larger than previous studies. Our method is able to keep the betweenness centrality measures up-to-date online, i.e., the time to update the measures is smaller than the inter-arrival time between two consecutive updates.

An automated approach to network features of protein structure ensembles

Abstract: Network theory applied to protein structures provides insights into numerous problems of biological relevance. The explosion in structural data available from PDB and simulations establishes a need to introduce a standalone-efficient program that assembles network concepts/parameters under one hood in an automated manner. Herein, we discuss the development/application of an exhaustive, user-friendly, standalone program package named PSN-Ensemble, which can handle structural ensembles generated through molecular dynamics (MD) simulation/NMR studies or from multiple X-ray structures. The novelty in network construction lies in the explicit consideration of side-chain interactions among amino acids. The program evaluates network parameters dealing with topological organization and long-range allosteric communication. The introduction of a flexible weighing scheme in terms of residue pairwise cross-correlation/interaction energy in PSN-Ensemble brings in dynamical/chemical knowledge into the network representation. Also, the results are mapped on a graphical display of the structure, allowing an easy access of network analysis to a general biological community. The potential of PSN-Ensemble toward examining structural ensemble is exemplified using MD trajectories of an ubiquitin-conjugating enzyme (UbcH5b). Furthermore, insights derived from network parameters evaluated using PSN-Ensemble for single-static structures of active/inactive states of β2-adrenergic receptor and the ternary tRNA complexes of tyrosyl tRNA synthetases (from organisms across kingdoms) are discussed. PSN-Ensemble is freely available from http://vishgraph.mbu.iisc.ernet.in/PSN-Ensemble/psn_index.html.

Identification of top-K nodes in large networks using Katz centrality

Abstract: Network theory concepts form the core of algorithms that are designed to uncover valuable insights from various datasets. Especially, network centrality measures such as Eigenvector centrality, Katz centrality, PageRank centrality etc., are used in retrieving top-K viral information propagators in social networks,while web page ranking in efficient information retrieval, etc. In this paper, we propose a novel method for identifying top-K viral information propagators from a reduced search space. Our algorithm computes the Katz centrality and Local average centrality values of each node and tests the values against two threshold (constraints) values. Only those nodes, which satisfy these constraints, form the search space for top-K propagators. Our proposed algorithm is tested against four datasets and the results show that the proposed algorithm is capable of reducing the number of nodes in search space at least by 70%. We also considered the parameter ( $$\alpha$$ and $$\beta$$ ) dependency of Katz centrality values in our experiments and established a relationship between the $$\alpha$$ values, number of nodes in search space and network characteristics. Later, we compare the top-K results of our approach against the top-K results of degree centrality.