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Closeness (graph Theory)
In graph theory and network theory, network analysis, indicators of centrality assign numbers or rankings to vertex (graph theory), 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 sociology, 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" ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Theory
In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph theory), vertices'' (also called ''nodes'' or ''points'') which are connected by ''Glossary of graph theory terms#edge, edges'' (also called ''arcs'', ''links'' or ''lines''). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics. Definitions Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures. Graph In one restricted but very common sense of the term, a graph is an ordered pair G=(V,E) comprising: * V, a Set (mathematics), set of vertices (also called nodes or points); * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alpha Centrality
Alpha (uppercase , lowercase ) is the first letter of the Greek alphabet. In the system of Greek numerals, it has a value of one. Alpha is derived from the Phoenician letter ''aleph'' , whose name comes from the West Semitic word for ' ox'. Letters that arose from alpha include the Latin letter and the Cyrillic letter . Uses Greek In Ancient Greek, alpha was pronounced and could be either phonemically long ( ː or short ( . Where there is ambiguity, long and short alpha are sometimes written with a macron and breve today: . * = ' "a time" * = ' "tongue" In Modern Greek, vowel length has been lost, and all instances of alpha simply represent the open front unrounded vowel . In the polytonic orthography of Greek, alpha, like other vowel letters, can occur with several diacritic marks: any of three accent symbols (), and either of two breathing marks (), as well as combinations of these. It can also combine with the iota subscript (). Greek grammar In the Attic– I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dense Matrix
In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify as sparse but a common criterion is that the number of non-zero elements is roughly equal to the number of rows or columns. By contrast, if most of the elements are non-zero, the matrix is considered dense. The number of zero-valued elements divided by the total number of elements (e.g., ''m'' × ''n'' for an ''m'' × ''n'' matrix) is sometimes referred to as the sparsity of the matrix. Conceptually, sparsity corresponds to systems with few pairwise interactions. For example, consider a line of balls connected by springs from one to the next: this is a sparse system, as only adjacent balls are coupled. By contrast, if the same line of balls were to have springs connecting each ball to all other balls, the system would correspond to a dense matrix. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Big Theta
Big ''O'' notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. Big O is a member of a family of notations invented by German mathematicians Paul Bachmann, Edmund Landau, and others, collectively called Bachmann–Landau notation or asymptotic notation. The letter O was chosen by Bachmann to stand for ''Ordnung'', meaning the order of approximation. In computer science, big O notation is used to classify algorithms according to how their run time or space requirements grow as the input size grows. In analytic number theory, big O notation is often used to express a bound on the difference between an arithmetical function and a better understood approximation; one well-known example is the remainder term in the prime number theorem. Big O notation is also used in many other fields to provide similar estimates. Big O notation characterizes functions according to their growth rat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Freeman Centralization
Freeman, free men, Freeman's or Freemans may refer to: Places United States * Freeman, Georgia, an unincorporated community * Freeman, Illinois, an unincorporated community * Freeman, Indiana, an unincorporated community * Freeman, South Dakota, a city * Freeman, Virginia, an unincorporated community * Freeman, Washington, an unincorporated community * Freeman, Wisconsin, a town * Freeman, Langlade County, Wisconsin, an unincorporated community * Freeman Island, an island in the state of Washington * Freeman Peak, a mountain in Idaho * Freeman Township, Michigan * Freeman Township, Freeborn County, Minnesota Norway * Freeman Strait (Freemansundet), a body of water People and fictional characters * Freeman (surname), includes a list of people and fictional characters * Freeman (given name), includes a list of people and fictional characters * A member of the Third Estate in medieval society (commoners) * Freeman, a member or an apprentice who has been granted freedom of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Node Influence Metric
In graph theory and network analysis, node influence metrics are measures that rank or quantify the influence of every node (also called vertex) within a graph. They are related to centrality indices. Applications include measuring the influence of each person in a social network, understanding the role of infrastructure nodes in transportation networks, the Internet, or urban networks, and the participation of a given node in disease dynamics. Origin and development The traditional approach to understanding node importance is via centrality indicators. Centrality indices are designed to produce a ranking which accurately identifies the most influential nodes. Since the mid 2000s, however, social scientists and network physicists have begun to question the suitability of centrality indices for understanding node influence. Centralities may indicate the most influential nodes, but they are rather less informative for the vast majority of nodes which are not highly influential. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Krackhardt Kite Graph
In graph theory, the Krackhardt kite graph is a simple graph with ten nodes. The graph is named after David Krackhardt, a researcher of social network theory. Krackhardt introduced the graph in 1990 to distinguish different concepts of centrality. It has the property that the vertex with maximum degree (labeled 3 in the figure, with degree 6), the vertex with maximum betweenness centrality (labeled 7), and the two vertices with maximum closeness centrality In a connected graph, closeness centrality (or closeness) of a node is a measure of centrality in a network, calculated as the reciprocal of the sum of the length of the shortest paths between the node and all other nodes in the graph. Thus, th ... (labeled 5 and 6) are all different from each other. References Individual graphs {{graph-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Authority Distribution
Authority distribution is a solution concept in cooperative game theory formulated by Lloyd Shapley and his doctoral student Xingwei Hu in 2003 to measure the authority and Power (social and political), power of players in well-defined hierarchical organizations. The concept provides a mathematical framework for quantifying how decision-making authority is distributed among individuals or units within hierarchical structures. Authority distribution generates the Shapley-Shubik power index as a special case and extends its application to more complex organizational settings. The theory builds upon Shapley's earlier work on the Shapley value, which earned him the Nobel Memorial Prize in Economic Sciences in 2012. Authority distribution can be used for ranking, strategic planning, and organizational design, providing quantitative insights into optimal decision-making structures and delegation of authority. Unlike traditional power indices, which primarily focus on voting systems, auth ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
