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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, the more central a node is, the ''closer'' it is to all other nodes. Closeness was defined by Bavelas (1950) as the reciprocal of the farness, that is: : C_B(x)= \frac, where d(y,x) is the distance (length of the shortest path) between vertices x and y. This unnormalised version of closeness is sometimes known as status. When speaking of closeness centrality, people usually refer to its normalized form which represents the average length of the shortest paths instead of their sum. It is generally given by the previous formula multiplied by N-1, where N is the number of nodes in the graph resulting in: : C(x)= \frac. The normalization of closeness simplifies the comparison of nodes in graphs of different sizes. For large graphs, the minu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Connected Component (graph Theory)
In graph theory, a component of an undirected graph is a connected subgraph that is not part of any larger connected subgraph. The components of any graph partition its vertices into disjoint sets, and are the induced subgraphs of those sets. A graph that is itself connected has exactly one component, consisting of the whole graph. Components are sometimes called connected components. The number of components in a given graph is an important graph invariant, and is closely related to invariants of matroids, topological spaces, and matrices. In random graphs, a frequently occurring phenomenon is the incidence of a giant component, one component that is significantly larger than the others; and of a percolation threshold, an edge probability above which a giant component exists and below which it does not. The components of a graph can be constructed in linear time, and a special case of the problem, connected-component labeling, is a basic technique in image analysis. Dy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strongly Connected Component
In the mathematics, mathematical theory of directed graphs, a graph is said to be strongly connected if every vertex is reachability, reachable from every other vertex. The strongly connected components of a directed graph form a partition of a set, partition into subgraph (graph theory), subgraphs that are themselves strongly connected. It is possible to test the strong connectivity (graph theory), connectivity of a graph, or to find its strongly connected components, in linear time (that is, Θ(''V'' + ''E'')). Definitions A directed graph is called strongly connected if there is a path (graph theory), path in each direction between each pair of vertices of the graph. That is, a path exists from the first vertex in the pair to the second, and another path exists from the second vertex to the first. In a directed graph ''G'' that may not itself be strongly connected, a pair of vertices ''u'' and ''v'' are said to be strongly connected to each other if there is a path in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Betweenness Centrality
In graph theory, betweenness 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, that is, there exists at least one path 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. 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 stand between each other. For example, in a telecommunications network, a node with higher b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Walk Closeness Centrality
Random walk closeness centrality is a measure of centrality in a network, which describes the average speed with which randomly walking processes reach a node from other nodes of the network. It is similar to the closeness centrality except that the farness is measured by the expected length of a random walk rather than by the shortest path. The concept was first proposed by White and Smyth (2003) under the name ''Markov centrality''. Intuition Consider a network with a finite number of nodes and a random walk process that starts in a certain node and proceeds from node to node along the edges. From each node, it chooses randomly the edge to be followed. In an unweighted network, the probability of choosing a certain edge is equal across all available edges, while in a weighted network it is proportional to the edge weights. A node is considered to be close to other nodes, if the random walk process initiated from any node of the network arrives to this particular node in relati ... [...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 d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hierarchical Closeness
Hierarchical closeness (HC) is a structural centrality measure used in network theory or 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 .... It is extended from closeness centrality to rank how centrally located a node is in a directed network. While the original closeness centrality of a directed network considers the most important node to be that with the least total distance from all other nodes, hierarchical closeness evaluates the most important node as the one which reaches the most nodes by the shortest paths. The hierarchical closeness explicitly includes information about the range of other nodes that can be affected by the given node. In a directed network G(V, A) where V is the set of nodes and A is the set of interactions, hierarchical closeness of a node i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Walk Closeness Centrality
Random walk closeness centrality is a measure of centrality in a network, which describes the average speed with which randomly walking processes reach a node from other nodes of the network. It is similar to the closeness centrality except that the farness is measured by the expected length of a random walk rather than by the shortest path. The concept was first proposed by White and Smyth (2003) under the name ''Markov centrality''. Intuition Consider a network with a finite number of nodes and a random walk process that starts in a certain node and proceeds from node to node along the edges. From each node, it chooses randomly the edge to be followed. In an unweighted network, the probability of choosing a certain edge is equal across all available edges, while in a weighted network it is proportional to the edge weights. A node is considered to be close to other nodes, if the random walk process initiated from any node of the network arrives to this particular node in relati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Mean
In mathematics, the harmonic mean is a kind of average, one of the Pythagorean means. It is the most appropriate average for ratios and rate (mathematics), rates such as speeds, and is normally only used for positive arguments. The harmonic mean is the multiplicative inverse, reciprocal of the arithmetic mean of the reciprocals of the numbers, that is, the generalized f-mean with f(x) = \frac. For example, the harmonic mean of 1, 4, and 4 is :\left(\frac\right)^ = \frac = \frac = 2\,. Definition The harmonic mean ''H'' of the positive real numbers x_1, x_2, \ldots, x_n is :H(x_1, x_2, \ldots, x_n) = \frac = \frac. It is the reciprocal of the arithmetic mean of the reciprocals, and vice versa: :\begin H(x_1, x_2, \ldots, x_n) &= \frac, \\ A(x_1, x_2, \ldots, x_n) &= \frac, \end where the arithmetic mean is A(x_1, x_2, \ldots, x_n) = \tfrac1n \sum_^n x_i. The harmonic mean is a Schur-concave function, and is greater than or equal to the minimum of its arguments: for positive a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetic Mean
In mathematics and statistics, the arithmetic mean ( ), arithmetic average, or just the ''mean'' or ''average'' is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results from an experiment, an observational study, or a Survey (statistics), survey. The term "arithmetic mean" is preferred in some contexts in mathematics and statistics because it helps to distinguish it from other types of means, such as geometric mean, geometric and harmonic mean, harmonic. Arithmetic means are also frequently used in economics, anthropology, history, and almost every other academic field to some extent. For example, per capita income is the arithmetic average of the income of a nation's Human population, population. While the arithmetic mean is often used to report central tendency, central tendencies, it is not a robust statistic: it is greatly influenced by outliers (Value (mathematics), values much larger or smaller than ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vito Latora
Vito Latora is an Italian physicist, currently Professor in Applied Mathematics (Chair of Complex Systems) at the School of Mathematical Sciences of the Queen Mary University of London. He is known for his works on complex systems, in particular on the structure and dynamics of complex networks. Career Latora received a PhD in physics from the University of Catania in Italy for a thesis in the field of theoretical nuclear physics entitled "''Multifragmentation, phase transitions and critical chaos in hot nuclei''". He conducted postdoctoral research at Massachusetts Institute of Technology (MIT) in the group of Michel Baranger, in the group of Eric Heller at Harvard University, and at Paris University XI. After his postdoctoral period, he joined the department of Physics of the University of Catania as an assistant professor in 2002. Since 2012, Vito Latora is Full Professor in Applied Mathematics (Chair in Complex Systems) at the Queen Mary University of London. Resear ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Massimo Marchiori
Massimo Marchiori (Padua, 1970) is an Italian people, Italian mathematician and computer scientist. Biography In July, 2004, he was awarded the TR35 prize by Technology Review (the best 35 researchers in the world under the age of 35). He is Professor in Computer Science at the University of Padua, and Research Scientist at MIT’s Computer Science and MIT Artificial Intelligence Laboratory, Artificial Intelligence Laboratory (CSAIL) in the World Wide Web Consortium. He was the creator of HyperSearch, a search engine where the results were based not only on single page ranks, but on the relationship between single pages and the rest of the Web. Afterwards, Google co-founders Larry Page and Sergey Brin cited HyperSearch when they introduced PageRank. He has been chief editor of the world standard for privacy on the Web (P3P), and co-author of the companion APPEL specification. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
