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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 man ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Loop (graph Theory)
In graph theory, a loop (also called a self-loop or a ''buckle'') is an edge that connects a vertex to itself. A simple graph contains no loops. Depending on the context, a graph or a multigraph may be defined so as to either allow or disallow the presence of loops (often in concert with allowing or disallowing multiple edges between the same vertices): * Where graphs are defined so as to ''allow'' loops and multiple edges, a graph without loops or multiple edges is often distinguished from other graphs by calling it a ''simple graph''. * Where graphs are defined so as to ''disallow'' loops and multiple edges, a graph that does have loops or multiple edges is often distinguished from the graphs that satisfy these constraints by calling it a ''multigraph'' or '' pseudograph''. In a graph with one vertex, all edges must be loops. Such a graph is called a bouquet. Degree For an undirected graph, the degree of a vertex is equal to the number of adjacent vertices. A special case ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lollipop Graph
In the mathematical discipline of graph theory, the (''m'',''n'')-lollipop graph is a special type of graph consisting of a complete graph (clique) on ''m'' vertices and a path graph on ''n'' vertices, connected with a bridge. The special case of the (''2n/3'',''n/3'')-lollipop graphs are known as graphs which achieve the maximum possible hitting time, cover time and commute time. See also * Barbell graph * Tadpole graph In the mathematical discipline of graph theory, the (''m'',''n'')-tadpole graph is a special type of graph consisting of a cycle graph on ''m'' (at least 3) vertices and a path graph on ''n'' vertices, connected with a bridge A bridge ... References Parametric families of graphs {{combin-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Return Times
Return may refer to: In business, economics, and finance * Return on investment (ROI), the financial gain after an expense. * Rate of return, the financial term for the profit or loss derived from an investment * Tax return, a blank document or template supplied by a government for use in the reporting of tax information * Product return, the process of bringing back merchandise to a retailer for a refund or exchange * Returns (economics), the benefit distributed to the owner of a factor of production * Abnormal return, denoting the difference in behaviour between one stock and the overall stock market * Taxes, where tax returns are forms submitted to taxation authorities In technology * Return (architecture), the receding edge of a flat face * Carriage return, a key on an alphanumeric keyboard commonly equated with the "enter" key * Return statement, a computer programming statement that ends a subroutine and resumes execution where the subroutine was called * Return code, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Deviation
In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. Standard deviation may be abbreviated SD, and is most commonly represented in mathematical texts and equations by the lower case Greek letter σ (sigma), for the population standard deviation, or the Latin letter '' s'', for the sample standard deviation. The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance. It is algebraically simpler, though in practice less robust, than the average absolute deviation. A useful property of the standard deviation is that, unlike the variance, it is expressed in the same unit as the data. The standard deviation o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aidong Zhang
Aidong Zhang is a computer scientist whose research topics include machine learning and bioinformatics. She is William Wulf Faculty Fellow and Professor of Computer Science at the University of Virginia, where she also holds affiliations with the Department of Biomedical Engineering and School of Data Science. Education and career Zhang earned her PhD in 1994 at Purdue University. She joined the department of computer science of the University at Buffalo as an assistant professor in 1994, became full professor in 2002, and was named University at Buffalo Distinguished Professor in 2012 and SUNY Distinguished Professor in 2014. She chaired the department from 2009 to 2015. After taking a leave from the department from 2015 to 2018 to serve as a program director for the National Science Foundation, she moved to the University of Virginia in 2019. She continues to be listed by the University at Buffalo as professor emerita. Zhang was the founding chair of the ACM Special Inter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Input-output Model
In computing, input/output (I/O, or informally io or IO) is the communication between an information processing system, such as a computer, and the outside world, possibly a human or another information processing system. Inputs are the signals or data received by the system and outputs are the signals or data sent from it. The term can also be used as part of an action; to "perform I/O" is to perform an input or output operation. are the pieces of hardware used by a human (or other system) to communicate with a computer. For instance, a keyboard or computer mouse is an input device for a computer, while monitors and printers are output devices. Devices for communication between computers, such as modems and network cards, typically perform both input and output operations. Any interaction with the system by a interactor is an input and the reaction the system responds is called the output. The designation of a device as either input or output depends on perspective. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Degree Distribution
In the study of graphs and networks, the degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability distribution of these degrees over the whole network. Definition The degree of a node in a network (sometimes referred to incorrectly as the connectivity) is the number of connections or edges the node has to other nodes. If a network is directed, meaning that edges point in one direction from one node to another node, then nodes have two different degrees, the in-degree, which is the number of incoming edges, and the out-degree, which is the number of outgoing edges. The degree distribution ''P''(''k'') of a network is then defined to be the fraction of nodes in the network with degree ''k''. Thus if there are ''n'' nodes in total in a network and ''n''''k'' of them have degree ''k'', we have P(k) = \frac. The same information is also sometimes presented in the form of a ''cumulative degree distribution'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph (discrete Mathematics)
In discrete mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called '' vertices'' (also called ''nodes'' or ''points'') and each of the related pairs of vertices is called an ''edge'' (also called ''link'' or ''line''). Typically, a graph is depicted in diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges. Graphs are one of the objects of study in discrete mathematics. The edges may be directed or undirected. For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this graph is undirected because any person ''A'' can shake hands with a person ''B'' only if ''B'' also shakes hands with ''A''. In contrast, if an edge from a person ''A'' to a person ''B'' means that ''A'' owes money to ''B'', th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
