Network theory

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

K-shell decomposition reveals hierarchical cortical organization of the human brain

Abstract: In recent years numerous attempts to understand the human brain were undertaken from a network point of view. A network framework takes into account the relationships between the different parts of the system and enables to examine how global and complex functions might emerge from network topology. Previous work revealed that the human brain features 'small world' characteristics and that cortical hubs tend to interconnect among themselves. However, in order to fully understand the topological structure of hubs one needs to go beyond the properties of a specific hub and examine the various structural layers of the network. To address this topic further, we applied an analysis known in statistical physics and network theory as k-shell decomposition analysis. The analysis was applied on a human cortical network, derived from MRI\DSI data of six participants. Such analysis enables us to portray a detailed account of cortical connectivity focusing on different neighborhoods of interconnected layers across the cortex. Our findings reveal that the human cortex is highly connected and efficient, and unlike the internet network contains no isolated nodes. The cortical network is comprised of a nucleus alongside shells of increasing connectivity that formed one connected giant component. All these components were further categorized into three hierarchies in accordance with their connectivity profile, with each hierarchy reflecting different functional roles. Such a model may explain an efficient flow of information from the lowest hierarchy to the highest one, with each step enabling increased data integration. At the top, the highest hierarchy (the nucleus) serves as a global interconnected collective and demonstrates high correlation with consciousness related regions, suggesting that the nucleus might serve as a platform for consciousness to emerge.

Effective co-betweenness centrality computation

Abstract: Betweenness centrality of vertices is essential in the analysis of social and information networks, and co-betweenness centrality is one of two natural ways to extend it to sets of vertices. Existing algorithms for co-betweenness centrality computation suffer from at least one of the following problems: i) their applicability is limited to special cases like sequences, sets of size two, and ii) they are not efficient in terms of time complexity. In this paper, we present efficient algorithms for co-betweenness centrality computation of any set or sequence of vertices in weighted and unweighted networks. We also develop effective methods for co-betweenness centrality computation of sets and sequences of edges. These results provide a clear and extensive view about the complexity of co-betweenness centrality computation for vertices and edges in weighted and un-weighted networks. Finally, we perform extensive experiments on real-world networks from different domains including social, information and communication networks, to show the empirical efficiency of the proposed methods.

Inference for Multiple Heterogeneous Networks with a Common Invariant Subspace

Abstract: The development of models and methodology for the analysis of data from multiple heterogeneous networks is of importance both in statistical network theory and across a wide spectrum of application domains. Although single-graph analysis is well-studied, multiple graph inference is largely unexplored, in part because of the challenges inherent in appropriately modeling graph differences and yet retaining sufficient model simplicity to render estimation feasible. This paper addresses exactly this gap, by introducing a new model, the common subspace independent-edge multiple random graph model, which describes a heterogeneous collection of networks with a shared latent structure on the vertices but potentially different connectivity patterns for each graph. The model encompasses many popular network representations, including the stochastic blockmodel. The model is both flexible enough to meaningfully account for important graph differences, and tractable enough to allow for accurate inference in multiple networks. In particular, a joint spectral embedding of adjacency matrices-the multiple adjacency spectral embedding-leads to simultaneous consistent estimation of underlying parameters for each graph. Under mild additional assumptions, the estimates satisfy asymptotic normality and yield improvements for graph eigenvalue estimation. In both simulated and real data, the model and the embedding can be deployed for a number of subsequent network inference tasks, including dimensionality reduction, classification, hypothesis testing, and community detection. Specifically, when the embedding is applied to a data set of connectomes constructed through diffusion magnetic resonance imaging, the result is an accurate classification of brain scans by human subject and a meaningful determination of heterogeneity across scans of different individuals.

Methodology of predicting novel key regulators in ovarian cancer network: a network theoretical approach

Abstract: Identification of key regulator/s in ovarian cancer (OC) network is important for potential drug target and prevention from this cancer. This study proposes a method to identify the key regulators of this network and their importance. The protein-protein interaction (PPI) network of ovarian cancer (OC) is constructed from curated 6 hundred genes from standard six important ovarian cancer databases (some of the genes are experimentally verified). We proposed a method to identify key regulators (KRs) from the complex ovarian cancer network based on the tracing of backbone hubs, which participate at all levels of organization, characterized by Newmann-Grivan community finding method. Knockout experiment, constant Potts model and survival analysis are done to characterize the importance of the key regulators in regulating the network. The PPI network of ovarian cancer is found to obey hierarchical scale free features organized by topology of heterogeneous modules coordinated by diverse leading hubs. The network and modular structures are devised by fractal rules with the absence of centrality-lethality rule, to enhance the efficiency of signal processing in the network and constituting loosely connected modules. Within the framework of network theory, we device a method to identify few key regulators (KRs) from a huge number of leading hubs, that are deeply rooted in the network, serve as backbones of it and key regulators from grassroots level to complete network structure. Using this method we could able to identify five key regulators, namely, AKT1, KRAS, EPCAM, CD44 and MCAM, out of which AKT1 plays central role in two ways, first it serves as main regulator of ovarian cancer network and second serves as key cross-talk agent of other key regulators, but exhibits disassortive property. The regulating capability of AKT1 is found to be highest and that of MCAM is lowest. The popularities of these key hubs change in an unpredictable way at different levels of organization and absence of these hubs cause massive amount of wiring energy/rewiring energy that propagate over all the network. The network compactness is found to increase as one goes from top level to bottom level of the network organization.

Status, networks, and opinions: A modular integration of two theories

Abstract: This chapter focuses on two theories in the landscape of research on social influence – status characteristics theory and social influence network theory – between which heretofore there has been little communication. We advance these two approaches by dovetailing them in a “modular integration” that retains the assumptions of each theory and extends their scope of application. Here, we concentrate on the extension of status characteristics theory to multiactor task-oriented groups and develop new insights on the effects of status characteristics in such groups. We address the implications for opinion changes of status differentiations in which some individuals are deemed more socially worthy and capable than others.