Topic
Network theory
About: Network theory is a research topic. Over the lifetime, 2257 publications have been published within this topic receiving 109864 citations.
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23 Jul 2019
TL;DR: A Monte Carlo method framework by which temporal graph algorithms that yield numerical or set-based results may be studied for conditions of stability is proposed and demonstrated by way of a geometric SST graph, which is defined based on the geometric random graph exhibiting Brownian motion of nodes.
Abstract: In numerous applications, spatiotemporal graphs are studied to exploit the structure of underlying data to characterize, control, or predict behavior. Nodes of these graphs exhibit spatiality, while edge connectivity and weighting may be derived from spatial conditions of the incident nodes. Because of the complexity added by the temporal dimension, these graphs are typically modeled in part as a stochastic processes. Though numerous application-defined spatiotemporal graphs with stochastic parameterizations exist, a general stochastic process for such graphs has not yet been formally defined in the literature. In an effort to move towards generalization, we offer a brief introduction to the Stochastic SpatioTemporal (SST) graph model, which describes a graph as a set of initially observed nodes and several sets of stochastic processes: one describing node motion, one describing edge connectivity, and one describing edge weight variation. We propose a Monte Carlo method framework by which temporal graph algorithms that yield numerical or set-based results may be studied for conditions of stability. We demonstrate such a framework by way of a geometric SST graph, which is defined based on the geometric random graph exhibiting Brownian motion of nodes. We offer results to show the points at which node movement and edge weight variation cause the geometric SST graph to become unstable for predicting least-cost paths. Finally, we discuss ongoing research projects and plans currently being undertaken to study and utilize stochastic properties of spatiotemporal network data.
01 Jan 2015
TL;DR: This chapter focuses on extant network dynamics theory and addresses the concepts of scaling, power laws, and fractals, which are prominent in both structural and dynamical behavior of complex networks.
Abstract: This chapter focuses on extant network dynamics theory. It explores the complex dynamics of structurally complex networks. The goal is a more complete understanding of real-world networks, and ecological networks in particular. First, the chapter addresses the concepts of scaling, power laws, and fractals, which are prominent in both structural and dynamical behavior of complex networks. After discussing the relationships among these three concepts, some introductory comments on spatial and temporal fractals are provided. (Details on fractals are provided in later chapters.) Next, the dynamics of network phase transitions are covered. The transition from an unconnected to a connected network, the phenomenon of network percolation, and other important aspects of network phase transitions are described and discussed. Network dynamics are then explored via examples of processes that take place on networks. These include epidemic processes, network failure/attack processes, macroevolution processes, and network growth processes.
Dissertation•
22 Aug 2013
TL;DR: An efficient algorithm with guaranteed error bound for approximating the centrality values of the nodes in a network is presented and the results show that the approaches work surprisingly well on real world networks.
Abstract: Social networks are nowadays a key factor shaping the way people interacting with each other. Therefore it is of great interest for researchers in industry and academia to analyse them. Among various methods, centrality measure and community detection are the two core approaches to uncover and understand the structure of networks. In this thesis, we propose a new centrality measure which emphasizes on locality. We develop a straightforward method for computing the centrality values of the nodes in a network. In order to apply to platforms in reality, which may have millions of users, we then present an efficient algorithm with guaranteed error bound for approximating the centrality values. Later in the thesis, we adopt the results on our new centrality measure to explore communities in a network. We evaluate our algorithms on several datasets. The results show that our approaches work surprisingly well on real world networks.
08 Jun 2005
TL;DR: A network model in which the communication between its elements can be established in various ways and each element has an “internal plasticity threshold” that, by setting the number of inputs and outputs, determines different network global topologies.
Abstract: We propose a network model in which the communication between its elements (cells, neurons and lymphocytes) can be established in various ways. The system evolution is driven by a set of equations that encodes various degrees of competition between elements. Each element has an “internal plasticity threshold” that, by setting the number of inputs and outputs, determines different network global topologies.