Network theory

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

Community detection for correlation matrices.

Abstract: Identifying groups of highly correlated units in a complex system is a notoriously challenging task. A new technique that adapts tools from network theory solves this problem and is used to map the mesoscopic structure of various stock markets.

Beyond Shannon: the quest for fundamental performance limits of wireless ad hoc networks

Abstract: We describe a new theoretical framework for determining fundamental performance limits of wireless ad hoc networks. The framework expands the traditional definition of Shannon capacity to incorporate notions of delay and outage. Novel tools are described for upper and lower bounding the network performance regions associated with these metrics under a broad range of assumptions about channel and network dynamics, state information, and network topologies. We also develop a flexible and dynamic interface between network applications and the network performance regions to obtain the best end-to-end performance. Our proposed framework for determining performance limits of wireless networks embraces an interdisciplinary approach to this challenging problem that incorporates Shannon Theory along with network theory, combinatorics, optimization, stochastic control, and game theory. Preliminary results of this approach are described and promising future directions of research are outlined.

Network structure of two-dimensional decaying isotropic turbulence

Abstract: The present paper reports on our effort to characterize vortical interactions in complex fluid flows through the use of network analysis. In particular, we examine the vortex interactions in two-dimensional decaying isotropic turbulence and find that the vortical-interaction network can be characterized by a weighted scale-free network. It is found that the turbulent flow network retains its scale-free behaviour until the characteristic value of circulation reaches a critical value. Furthermore, we show that the two-dimensional turbulence network is resilient against random perturbations, but can be greatly influenced when forcing is focused towards the vortical structures, which are categorized as network hubs. These findings can serve as a network-analytic foundation to examine complex geophysical and thin-film flows and take advantage of the rapidly growing field of network theory, which complements ongoing turbulence research based on vortex dynamics, hydrodynamic stability, and statistics. While additional work is essential to extend the mathematical tools from network analysis to extract deeper physical insights of turbulence, an understanding of turbulence based on the interaction-based network-theoretic framework presents a promising alternative in turbulence modelling and control efforts.

Towards a methodology for validation of centrality measures in complex networks.

Abstract: Background Living systems are associated with Social networks — networks made up of nodes, some of which may be more important in various aspects as compared to others. While different quantitative measures labeled as “centralities” have previously been used in the network analysis community to find out influential nodes in a network, it is debatable how valid the centrality measures actually are. In other words, the research question that remains unanswered is: how exactly do these measures perform in the real world? So, as an example, if a centrality of a particular node identifies it to be important, is the node actually important?