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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TL;DR: Several choices of the functions describing the creation and destruction processes of entanglement junctions in the Yamamoto network theory of concentrated polymer solutions have been examined as discussed by the authors, and it is demonstrated that the moments of the distribution function describing the network conformation can be solved for analytically.
Abstract: Several choices of the functions describing the creation and destruction processes of entanglement junctions in the Yamamoto network theory of concentrated polymer solutions have been examined. These choices are simple functions of the extension of the network segments bridging the entanglement points and it is demonstrated that the moments of the distribution function describing the network conformation can be solved for analytically. This has been done for a wide range of two-dimensional flows, both for the steady state and transient start-up and relaxation problems. The macroscopic stress tensor and flow birefringence are calculated and a variety of nonlinear effects are predicted and discussed.
20 citations
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18 Aug 2014TL;DR: This paper proposes the first measure of node centrality that takes into account the community structure of the underlying network, and proposes a generalization of the Owen value—a well-known solution concept from cooperative game theory to study games with a priori-given unions of players.
Abstract: There is currently much interest in the problem of measuring the centrality of nodes in networks/graphs; such measures have a range of applications, from social network analysis, to chemistry and biology. In this paper we propose the first measure of node centrality that takes into account the community structure of the underlying network. Our measure builds upon the recent literature on game-theoretic centralities, where solution concepts from cooperative game theory are used to reason about importance of nodes in the network. To allow for flexible modelling of community structures, we propose a generalization of the Owen value—a well-known solution concept from cooperative game theory to study games with a priori-given unions of players. As a result we obtain the first measure of centrality that accounts for both the value of an individual node's relationships within the network and the quality of the community this node belongs to.
19 citations
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TL;DR: This introductory chapter gives an overview of the ideas that the field of temporal networks has brought forward in the last decade and places the contributions to the current volume on this map of temporal-network approaches.
Abstract: The study of temporal networks is motivated by the simple and important observation that just as network structure can affect dynamics, so can structure in time, and just as network topology can teach us about the system in question, so can its temporal characteristics. In many cases, leaving out either one of these components would lead to an incomplete understanding of the system or poor predictions. Including time into network modeling, we argue, inevitably leads researchers away from the trodden paths of network science. Temporal network theory requires something different—new methods, new concepts, new questions—compared to static networks. In this introductory chapter, we give an overview of the ideas that the field of temporal networks has brought forward in the last decade. We also place the contributions to the current volume on this map of temporal-network approaches.
19 citations
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TL;DR: NWRank provides a new inexpensive way to rank nodes and links of a network, which has practical applications, particularly to prioritize resource allocation for upgrade of hierarchical and distributed networks, as well as to support decision making in the design of networks, where node and link importance depend on a balance of local and global integrity.
Abstract: This study proposes a novel Normalized Wide network Ranking algorithm (NWRank) that has the advantage of ranking nodes and links of a network simultaneously. This algorithm combines the mutual reinforcement feature of Hypertext Induced Topic Selection (HITS) and the weight normalization feature of PageRank. Relative weights are assigned to links based on the degree of the adjacent neighbors and the Betweenness Centrality instead of assigning the same weight to every link as assumed in PageRank. Numerical experiment results show that NWRank performs consistently better than HITS, PageRank, eigenvector centrality, and edge betweenness from the perspective of network connectivity and approximate network flow, which is also supported by comparisons with the expensive N-1 benchmark removal criteria based on network efficiency. Furthermore, it can avoid some problems, such as the Tightly Knit Community effect, which exists in HITS. NWRank provides a new inexpensive way to rank nodes and links of a network, which has practical applications, particularly to prioritize resource allocation for upgrade of hierarchical and distributed networks, as well as to support decision making in the design of networks, where node and link importance depend on a balance of local and global integrity.
19 citations
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TL;DR: In this paper, a principled generalization of network centrality measures that is valid for any eigenvector-based centrality measure is introduced, and the concepts of marginal and conditional centrality are introduced to facilitate the study of centrality trajectories over time.
Abstract: Numerous centrality measures have been developed to quantify the importances of nodes in time-independent networks, and many of them can be expressed as the leading eigenvector of some matrix. With the increasing availability of network data that changes in time, it is important to extend such eigenvector-based centrality measures to time-dependent networks. In this paper, we introduce a principled generalization of network centrality measures that is valid for any eigenvector-based centrality. We consider a temporal network with N nodes as a sequence of T layers that describe the network during different time windows, and we couple centrality matrices for the layers into a supra-centrality matrix of size NTxNT whose dominant eigenvector gives the centrality of each node i at each time t. We refer to this eigenvector and its components as a joint centrality, as it reflects the importances of both the node i and the time layer t. We also introduce the concepts of marginal and conditional centralities, which facilitate the study of centrality trajectories over time. We find that the strength of coupling between layers is important for determining multiscale properties of centrality, such as localization phenomena and the time scale of centrality changes. In the strong-coupling regime, we derive expressions for time-averaged centralities, which are given by the zeroth-order terms of a singular perturbation expansion. We also study first-order terms to obtain first-order-mover scores, which concisely describe the magnitude of nodes' centrality changes over time. As examples, we apply our method to three empirical temporal networks: the United States Ph.D. exchange in mathematics, costarring relationships among top-billed actors during the Golden Age of Hollywood, and citations of decisions from the United States Supreme Court.
19 citations