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Betweenness Centrality
In graph theory, betweenness centrality (or "betweeness centrality") is a measure of centrality in a graph based on shortest paths. For every pair of vertices in a connected graph, there exists at least one shortest path between the vertices such that either the number of edges that the path passes through (for unweighted graphs) or the sum of the weights of the edges (for weighted graphs) is minimized. The betweenness centrality for each vertex is the number of these shortest paths that pass through the vertex. Betweenness centrality was devised as a general measure of centrality: it applies to a wide range of problems in network theory, including problems related to social networks, biology, transport and scientific cooperation. Although earlier authors have intuitively described centrality as based on betweenness, gave the first formal definition of betweenness centrality. Betweenness centrality finds wide application in network theory; it represents the degree to which nodes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Betweenness
Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties *Graph (topology), a topological space resembling a graph in the sense of discrete mathematics *Graph of a function *Graph of a relation *Graph paper *Chart, a means of representing data (also called a graph) Computing *Graph (abstract data type), an abstract data type representing relations or connections *graph (Unix), Unix command-line utility *Conceptual graph, a model for knowledge representation and reasoning Other uses *HMS Graph, HMS ''Graph'', a submarine of the UK Royal Navy See also *Complex network *Graf *Graff (other) *Graph database *Grapheme, in linguistics *Graphemics *Graphic (other) *-graphy (suffix from the Greek for "describe," "write" or "draw") *List of information graphics software *Statistical graphics {{Disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Social Network Analysis
Social network analysis (SNA) is the process of investigating social structures through the use of networks and graph theory. It characterizes networked structures in terms of ''nodes'' (individual actors, people, or things within the network) and the ''ties'', ''edges'', or ''links'' (relationships or interactions) that connect them. Examples of social structures commonly visualized through social network analysis include social media networks, memes spread, information circulation, friendship and acquaintance networks, business networks, knowledge networks, difficult working relationships, social networks, collaboration graphs, kinship, disease transmission, and sexual relationships. These networks are often visualized through ''sociograms'' in which nodes are represented as points and ties are represented as lines. These visualizations provide a means of qualitatively assessing networks by varying the visual representation of their nodes and edges to reflect attributes of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Network Theory
Network theory is the study of graphs as a representation of either symmetric relations or asymmetric relations between discrete objects. In computer science and network science, network theory is a part of graph theory: a network can be defined as a graph in which nodes and/or edges have attributes (e.g. names). Network theory has applications in many disciplines including statistical physics, particle physics, computer science, electrical engineering, biology, archaeology, economics, finance, operations research, climatology, ecology, public health, sociology, and neuroscience. Applications of network theory include logistical networks, the World Wide Web, Internet, gene regulatory networks, metabolic networks, social networks, epistemological networks, etc.; see List of network theory topics for more examples. Euler's solution of the Seven Bridges of Königsberg problem is considered to be the first true proof in the theory of networks. Network optimization Network pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scientific Reports
''Scientific Reports'' is a peer-reviewed open-access scientific mega journal published by Nature Portfolio, covering all areas of the natural sciences. The journal was established in 2011. The journal states that their aim is to assess solely the scientific validity of a submitted paper, rather than its perceived importance, significance, or impact. In September 2016, the journal became the largest in the world by number of articles, overtaking '' PLOS ONE''. Abstracting and indexing The journal is abstracted and indexed in the Chemical Abstracts Service, the Science Citation Index Expanded, and selectively in Index Medicus/MEDLINE/PubMed. According to the ''Journal Citation Reports'', the journal has a 2021 impact factor 4.996. Reviewing policy The ''Guide to Referees'' states that to be published, "a paper must be scientifically valid and technically sound in methodology and analysis", and reviewers have to ensure manuscripts "are not assessed based on their perceived impor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oxford University Press
Oxford University Press (OUP) is the university press of the University of Oxford. It is the largest university press in the world, and its printing history dates back to the 1480s. Having been officially granted the legal right to print books by decree in 1586, it is the second oldest university press after Cambridge University Press. It is a department of the University of Oxford and is governed by a group of 15 academics known as the Delegates of the Press, who are appointed by the vice-chancellor of the University of Oxford. The Delegates of the Press are led by the Secretary to the Delegates, who serves as OUP's chief executive and as its major representative on other university bodies. Oxford University Press has had a similar governance structure since the 17th century. The press is located on Walton Street, Oxford, opposite Somerville College, in the inner suburb of Jericho. For the last 500 years, OUP has primarily focused on the publication of pedagogical texts and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harvard University Press
Harvard University Press (HUP) is a publishing house established on January 13, 1913, as a division of Harvard University, and focused on academic publishing. It is a member of the Association of American University Presses. After the retirement of William P. Sisler in 2017, the university appointed as Director George Andreou. The press maintains offices in Cambridge, Massachusetts near Harvard Square, and in London, England. The press co-founded the distributor TriLiteral LLC with MIT Press and Yale University Press. TriLiteral was sold to LSC Communications in 2018. Notable authors published by HUP include Eudora Welty, Walter Benjamin, E. O. Wilson, John Rawls, Emily Dickinson, Stephen Jay Gould, Helen Vendler, Carol Gilligan, Amartya Sen, David Blight, Martha Nussbaum, and Thomas Piketty. The Display Room in Harvard Square, dedicated to selling HUP publications, closed on June 17, 2009. Related publishers, imprints, and series HUP owns the Belknap Press imprint, whi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proceedings Of The National Academy Of Sciences Of The United States Of America
''Proceedings of the National Academy of Sciences of the United States of America'' (often abbreviated ''PNAS'' or ''PNAS USA'') is a peer-reviewed multidisciplinary scientific journal. It is the official journal of the National Academy of Sciences, published since 1915, and publishes original research, scientific reviews, commentaries, and letters. According to ''Journal Citation Reports'', the journal has a 2021 impact factor of 12.779. ''PNAS'' is the second most cited scientific journal, with more than 1.9 million cumulative citations from 2008 to 2018. In the mass media, ''PNAS'' has been described variously as "prestigious", "sedate", "renowned" and "high impact". ''PNAS'' is a delayed open access journal, with an embargo period of six months that can be bypassed for an author fee ( hybrid open access). Since September 2017, open access articles are published under a Creative Commons license. Since January 2019, ''PNAS'' has been online-only, although print issues are ava ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Centrality
In graph theory and network analysis, indicators of centrality assign numbers or rankings to nodes within a graph corresponding to their network position. Applications include identifying the most influential person(s) in a social network, key infrastructure nodes in the Internet or urban networks, super-spreaders of disease, and brain networks. Centrality concepts were first developed in social network analysis, and many of the terms used to measure centrality reflect their sociological origin.Newman, M.E.J. 2010. ''Networks: An Introduction.'' Oxford, UK: Oxford University Press. Definition and characterization of centrality indices Centrality indices are answers to the question "What characterizes an important vertex?" The answer is given in terms of a real-valued function on the vertices of a graph, where the values produced are expected to provide a ranking which identifies the most important nodes. The word "importance" has a wide number of meanings, leading to many diffe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cut (graph Theory)
In graph theory, a cut is a partition of the vertices of a graph into two disjoint subsets. Any cut determines a cut-set, the set of edges that have one endpoint in each subset of the partition. These edges are said to cross the cut. In a connected graph, each cut-set determines a unique cut, and in some cases cuts are identified with their cut-sets rather than with their vertex partitions. In a flow network, an s–t cut is a cut that requires the ''source'' and the ''sink'' to be in different subsets, and its ''cut-set'' only consists of edges going from the source's side to the sink's side. The ''capacity'' of an s–t cut is defined as the sum of the capacity of each edge in the ''cut-set''. Definition A cut is a partition of of a graph into two subsets and . The cut-set of a cut is the set of edges that have one endpoint in and the other endpoint in . If and are specified vertices of the graph , then an cut is a cut in which belongs to the set and belongs to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Connectivity (graph Theory)
In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more isolated subgraphs. It is closely related to the theory of network flow problems. The connectivity of a graph is an important measure of its resilience as a network. Connected vertices and graphs In an undirected graph , two '' vertices'' and are called connected if contains a path from to . Otherwise, they are called disconnected. If the two vertices are additionally connected by a path of length , i.e. by a single edge, the vertices are called adjacent. A graph is said to be connected if every pair of vertices in the graph is connected. This means that there is a path between every pair of vertices. An undirected graph that is not connected is called disconnected. An undirected graph ''G'' is therefore disconnected if there exist two vertices ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strahler Number
In mathematics, the Strahler number or Horton–Strahler number of a mathematical tree is a numerical measure of its branching complexity. These numbers were first developed in hydrology by and ; in this application, they are referred to as the Strahler stream order and are used to define stream size based on a hierarchy of tributaries. They also arise in the analysis of L-systems and of hierarchical biological structures such as (biological) trees and animal respiratory and circulatory systems, in register allocation for compilation of high-level programming languages and in the analysis of social networks. Alternative stream ordering systems have been developed by Shreve and Hodgkinson et al.Hodgkinson, J.H., McLoughlin, S. & Cox, M.E. 2006. The influence of structural grain on drainage in a metamorphic sub-catchment: Laceys Creek, southeast Queensland, Australia. Geomorphology, 81: 394–407. A statistical comparison of Strahler and Shreve systems, together with an analysis of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological Complexity
In mathematics, topological complexity of a topological space ''X'' (also denoted by TC(''X'')) is a topological invariant closely connected to the motion planning problem, introduced by Michael Farber in 2003. Definition Let ''X'' be a topological space and PX=\ be the space of all continuous paths in ''X''. Define the projection \pi: PX\to\,X\times X by \pi(\gamma)=(\gamma(0), \gamma(1)). The topological complexity is the minimal number ''k'' such that *there exists an open cover \_^k of X\times X, *for each i=1,\ldots,k, there exists a local section s_i:\,U_i\to\, PX. Examples *The topological complexity: TC(''X'') = 1 if and only if ''X'' is contractible. *The topological complexity of the sphere S^n is 2 for ''n'' odd and 3 for ''n'' even. For example, in the case of the circle S^1, we may define a path between two points to be the geodesic between the points, if it is unique. Any pair of antipodal points can be connected by a counter-clockwise path. *If F(\R^m,n) i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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