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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] |
Graph Theory
In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are connected by '' edges'' (also called ''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 of vertices (also called nodes or points); * E \subseteq \, a set of edges (also called links or lines), which are unordered pairs of vertices (that is, an edge is associated with t ... [...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] |
Vertex (graph Theory)
In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of vertices). In a diagram of a graph, a vertex is usually represented by a circle with a label, and an edge is represented by a line or arrow extending from one vertex to another. From the point of view of graph theory, vertices are treated as featureless and indivisible objects, although they may have additional structure depending on the application from which the graph arises; for instance, a semantic network is a graph in which the vertices represent concepts or classes of objects. The two vertices forming an edge are said to be the endpoints of this edge, and the edge is said to be incident to the vertices. A vertex ''w'' is said to be ad ... [...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] |
Social Network
A social network is a social structure made up of a set of social actors (such as individuals or organizations), sets of dyadic ties, and other social interactions between actors. The social network perspective provides a set of methods for analyzing the structure of whole social entities as well as a variety of theories explaining the patterns observed in these structures. The study of these structures uses social network analysis to identify local and global patterns, locate influential entities, and examine network dynamics. Social networks and the analysis of them is an inherently interdisciplinary academic field which emerged from social psychology, sociology, statistics, and graph theory. Georg Simmel authored early structural theories in sociology emphasizing the dynamics of triads and "web of group affiliations". Jacob Moreno is credited with developing the first sociograms in the 1930s to study interpersonal relationships. These approaches were mathematically formalize ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transport Network
A transport network, or transportation network, is a network or graph in geographic space, describing an infrastructure that permits and constrains movement or flow. Examples include but are not limited to road networks, railways, air routes, pipelines, aqueducts, and power lines. The digital representation of these networks, and the methods for their analysis, is a core part of spatial analysis, geographic information systems, public utilities, and transport engineering. Network analysis is an application of the theories and algorithms of graph theory and is a form of proximity analysis. History The applicability of graph theory to geographic phenomena was recognized as an early date. In fact, many of the early problems and theories undertaken by graph theorists were inspired by geographic situations, such as the Seven Bridges of Königsberg problem, which was one of the original foundations of graph theory when it was solved by Leonhard Euler in 1736. In the 1970s, the co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Internet
The Internet (or internet) is the global system of interconnected computer networks that uses the Internet protocol suite (TCP/IP) to communicate between networks and devices. It is a '' network of networks'' that consists of private, public, academic, business, and government networks of local to global scope, linked by a broad array of electronic, wireless, and optical networking technologies. The Internet carries a vast range of information resources and services, such as the inter-linked hypertext documents and applications of the World Wide Web (WWW), electronic mail, telephony, and file sharing. The origins of the Internet date back to the development of packet switching and research commissioned by the United States Department of Defense in the 1960s to enable time-sharing of computers. The primary precursor network, the ARPANET, initially served as a backbone for interconnection of regional academic and military networks in the 1970s to enable resource shari ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Urban Network
, also referred to as , is one of the Japan Railways Group (JR Group) companies and operates in western Honshu. It has its headquarters in Kita-ku, Osaka. It is listed in the Tokyo Stock Exchange, is a constituent of the TOPIX Large70 index, and is also one of only three Japan Railways Group constituents of the Nikkei 225 index: the others are East Japan Railway Company, JR East and Central Japan Railway Company, JR Central. It was also listed in the Nagoya Stock Exchange, Nagoya and Fukuoka Stock Exchange, Fukuoka stock exchanges until late 2020. Lines Shinkansen * Hokuriku Shinkansen ( - ) * San'yō Shinkansen * Hakata Minami Line :: Officially not a Shinkansen JR-West's highest-grossing line is the Sanyo Shinkansen high-speed rail line between Osaka and Fukuoka, Fukuoka, Fukuoka. The Sanyo Shinkansen alone accounts for about 40% of JR-West's passenger revenues. The company also operates Hakata Minami Line, a short commuter line with Shinkansen trains in Fukuoka, Fukuoka, Fukuo ... [...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] |
Force Of Infection
In epidemiology, force of infection (denoted \lambda) is the rate at which susceptible individuals acquire an infectious disease. Because it takes account of susceptibility it can be used to compare the rate of transmission between different groups of the population for the same infectious disease, or even between different infectious diseases. That is to say, \lambda is directly proportional to \beta; the effective transmission rate. : \lambda = \frac Such a calculation is difficult because not all new infections are reported, and it is often difficult to know how many susceptibles were exposed. However, \lambda can be calculated for an infectious disease in an endemic state if homogeneous mixing of the population and a rectangular population distribution (such as that generally found in developed countries), rather than a pyramid, is assumed. In this case, \lambda is given by: : \lambda = \frac where A is the average age of infection. In other words, A is the avera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Self-avoiding Walk
In mathematics, a self-avoiding walk (SAW) is a sequence of moves on a lattice (a lattice path) that does not visit the same point more than once. This is a special case of the graph theoretical notion of a path. A self-avoiding polygon (SAP) is a closed self-avoiding walk on a lattice. Very little is known rigorously about the self-avoiding walk from a mathematical perspective, although physicists have provided numerous conjectures that are believed to be true and are strongly supported by numerical simulations. In computational physics, a self-avoiding walk is a chain-like path in or with a certain number of nodes, typically a fixed step length and has the property that it doesn't cross itself or another walk. A system of SAWs satisfies the so-called excluded volume condition. In higher dimensions, the SAW is believed to behave much like the ordinary random walk. SAWs and SAPs play a central role in the modeling of the topological and knot-theoretic behavior of thread- a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compartmental Models In Epidemiology
Compartmental models are a very general modelling technique. They are often applied to the mathematical modelling of infectious diseases. The population is assigned to compartments with labels – for example, S, I, or R, (Susceptible, Infectious, or Recovered). People may progress between compartments. The order of the labels usually shows the flow patterns between the compartments; for example SEIS means susceptible, exposed, infectious, then susceptible again. The origin of such models is the early 20th century, with important works being that of Ross in 1916, Ross and Hudson in 1917, Kermack and McKendrick in 1927 and Kendall in 1956. The Reed-Frost model was also a significant and widely-overlooked ancestor of modern epidemiological modelling approaches. The models are most often run with ordinary differential equations (which are deterministic), but can also be used with a stochastic (random) framework, which is more realistic but much more complicated to analyze. Models ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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