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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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Journal ArticleDOI
TL;DR: Approaches of graph theory to some of the problems of network analysis and synthesis, starting with the early days of network theory, and contributions in the field of topological synthesis of pure resistive networks are described.
Abstract: This paper describes applications of graph theory to some of the problems of network analysis and synthesis, starting with the early days of network theory. The first section is devoted to the classical results related to the topological analysis of linear, passive, and transfornerless networks. Then it goes over to contributions dealing with generalization of these methods to networks with mutual couplings and active elements. Appearance of integrated circuits and digital computers provided both motivation and means for studying large-scale systems. A part of the paper is devoted to publications on large-scale network analysis dealing with diacoptics and graph theoretic methods for defining efficient Gaussian elimination algorithms for solution of sparse sets of linear algebraic equations. The part on topological synthesis starts with the early results dealing with relations between the structure and the properties of passive, reciprocal networks without mutual inductances. The last section is devoted to contributions in the field of topological synthesis of pure resistive networks dealing with such topics as conditions of realizability, minimal realizations and bounds on the number of port-terminals.

14 citations

Journal ArticleDOI
TL;DR: An algorithm allowing to find an approximate solution to the optimization problem of graph reduction is derived and it is shown that, if the initial network is a flow network, it is possible to design the algorithm such that the output remains aflow network.
Abstract: This paper deals with a particular problem of graph reduction. The reduced graph is aimed to have a particular structure, namely to be scale-free. To this end, we define a metric to measure the scale-freeness by measuring the difference between the degree distribution and the scale-free degree distribution. The reduction is made under constraints to preserve consistency with the initial graph. In particular, the reduced graph preserves the eigenvector centrality of the initial graph. We study the optimization problem and, based on the gained insights, we derive an algorithm allowing to find an approximate solution. We also show that, if the initial network is a flow network, it is possible to design the algorithm such that the output remains a flow network. Experimental results are then presented to optimally choose the parameters of the algorithm suggesting that, by tuning a parameter, it is possible to speed up the algorithm with a comparable efficiency. Finally, the algorithm is applied to an example of large physical network: the Grenoble urban traffic network.

14 citations

Journal ArticleDOI
TL;DR: In this article, the authors make extensive use of the Java Universal Network/Graph Framework (JUNG) via J/Link technology and facilitate communication of Mathematica graph structures to other network analysis programs such as Pajek by developing methods of import and export using GraphML.
Abstract: In common law jurisdictions such as the United States, courts frequently resolve disputes by citation and analysis of prior legal cases. The law may thus be thought of as a giant network containing textual information embedded in cases (nodes) and relationship information called citations (arcs) going from node to node. In recent years, the science of studying networks has developed [1] but, while there have been some primitive attempts to look at subsets of the vast legal network, until recently there has been little done to take advantage of modern technology and network theory. This article borrows techniques developed largely in sociology [2, 3] and physics and uses modern technology to learn about the law simply by studying its network structure. The article makes extensive use of the Java Universal Network/Graph Framework (JUNG) [4] via J/Link technology and facilitates communication of Mathematica graph structures to other network analysis programs such as Pajek by developing methods of import and export using GraphML. Although this article focuses on tool building, it is my hope that these efforts, along with pending publications on legal networks by Professor Thomas A. Smith of the University of San Diego Law School [5] and Professors James H. Fowler and Sangick Jeon of the University of California, Davis [6], will catalyze a set of studies in this field that will expand to cover other judicial systems and yet more sophisticated analysis of network information.

14 citations

Journal ArticleDOI
TL;DR: An under-explored area in Everett and Borgatti's work is in how this method can be applied to centrality problems; an issue is sought to begin to address here.
Abstract: Research using techniques from social network analysis have expanded dramatically in recent years. The availability of network data and the recognition that social network techniques can provide an...

14 citations

Journal Article
TL;DR: The term phenomcnological network theory (PNT) was coined by as mentioned in this paper to describe the interplay of meaning and network structure in the network of its authors, and is applied to itself by descri-bing the relationship between meaning and structure in its authors' networks.
Abstract: The term phenomcnological network theory school invisible college<. Phenomenological Network Theory is thus applied to itself by descri-bing the interplay of meaning and network structure in the network of its authors. The following questions are examined: Are the authors of this approach closely interlinked? Is there a clear core in the network or a differentiation into various subgroups? Is there a common collective identity? How does the approach emerge from the combination of various theoretical strands and in opposition to other strands in sociology? These questions are examined drawing on the various methods typical of the research associated with Phenomenological Network Theory. The essay comprises a narrative account of the history of the approach (in the context of other sociological theories), a formal analysis of the network of authors, and a qualitative analysis of interviews with the main authors.

14 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202319
202240
202175
2020109
201989
2018115