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Rich-club Coefficient
The rich-club coefficient is a metric on graphs and networks, designed to measure the extent to which well-connected nodes also connect to each other. Networks which have a relatively high rich-club coefficient are said to demonstrate the rich-club effect and will have many connections between nodes of high degree. The rich-club coefficient was first introduced in 2004 in a paper studying Internet topology.Mattia Gasparini, Javier Luis Canovas Izquierdo, Robert Clariso, Marco Brambilla, Jordi Cabot''Analyzing Rich-Club Behavior in Open Source Projects'' OpenSym 2019 proceedings The "Rich-club" effect has been measured and noted on scientific collaboration networks and air transportation networks. It has been shown to be significantly lacking on protein interaction networks. Definition Non-normalized form The rich-club coefficient was first introduced as an unscaled metric parametrized by node degree ranks. More recently, this has been updated to be parameterized in terms o ... [...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 (mathematics), set of objects in which some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called ''Vertex (graph theory), 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'' m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Network
In the context of network theory, a complex network is a graph (network) with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often occur in networks representing real systems. The study of complex networks is a young and active area of scientific research (since 2000) inspired largely by empirical findings of real-world networks such as computer networks, biological networks, technological networks, brain networks, climate networks and social networks. Definition Most social, biological, and technological networks display substantial non-trivial topological features, with patterns of connection between their elements that are neither purely regular nor purely random. Such features include a heavy tail in the degree distribution, a high clustering coefficient, assortativity or disassortativity among vertices, community structure, and hierarchical structure. In the case of directed networks these feat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Internet Topology
World Wide Web topology is the network topology of the World Wide Web, as seen as a network of web pages connected by hyperlinks. The Jellyfish and Bow Tie models are two attempts at modeling the topology of hyperlinks between web pages. Models of web page topology Jellyfish Model The simplistic Jellyfish model of the World Wide Web centers around a large strongly connected core of high-degree web pages that form a clique; pages such that there is a path from any page within the core to any other page. In other words, starting from any node within the core, it is possible to visit any other node in the core just by clicking hyperlinks. From there, a distinction is made between pages of single degree and those of higher order degree. Pages with many links form rings around the center, with all such pages that are a single link away from the core making up the first ring, all such pages that are two links away from the core making up the second ring, and so on. Then from each rin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
OpenSym
OpenSym is a shorthand for International Symposium on Open Collaboration, formerly International Symposium on Wikis and Open Collaboration, also formerly WikiSym or the Wiki Symposium, a conference dedicated to wiki research and practice. In 2014, the name of the conference was changed from WikiSym to OpenSym to reflect a broadening of scope from wiki and Wikipedia research and practice to open collaboration research, including wikis and Wikipedia research, but also free/libre/open source, open data, etc. research. The conference series is held in-cooperation with ACM SIGWEB and ACM SIGSOFT and its proceedings are published in the ACM Digital Library. Overview of conferences, 2005–present History ; WikiSym 2005 WikiSym 2005 was co-located with ACM OOPSLA 2005, held in San Diego, California, US, 14–16 October 2005. Speakers included Ward Cunningham, Jimmy Wales, Ross Mayfield and Sunir Shah. Sponsors of the event included Google. Conference chair was Dirk Riehle. ; WikiSy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biological Network
A biological network is a method of representing systems as complex sets of binary interactions or relations between various biological entities. In general, networks or graphs are used to capture relationships between entities or objects. A typical graphing representation consists of a set of nodes connected by edges. History of networks As early as 1736 Leonhard Euler analyzed a real-world issue known as the Seven Bridges of Königsberg, which established the foundation of graph theory. From the 1930's-1950's the study of random graphs were developed. During the mid 1990's, it was discovered that many different types of "real" networks have structural properties quite different from random networks. In the late 2000's, scale-free and small-world networks began shaping the emergence of systems biology, network biology, and network medicinIn 2014, graph theoretical methods were used bFrank Emmert-Streibto analyze biological networks. In the 1980s, researchers started v ... [...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'', the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structural Cut-off
The structural cut-off is a concept in network science which imposes a degree cut-off in the degree distribution of a finite size network due to structural limitations (such as the simple graph property). Networks with vertices with degree higher than the structural cut-off will display structural disassortativity. Definition The structural cut-off is a maximum degree cut-off that arises from the structure of a finite size network. Let E_ be the number of edges between all vertices of degree k and k' if k \neq k', and twice the number if k=k'. Given that multiple edges between two vertices are not allowed, E_ is bounded by the maximum number of edges between two degree classes m_ . Then, the ratio can be written : r_ \equiv \frac = \frac , where \langle k \rangle is the average degree of the network, N is the total number of vertices, P(k) is the probability a randomly chosen vertex will have degree k, and P(k,k') = E_/\langle k \rangle N is the probability that a randomly p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Assortativity
Assortativity, or assortative mixing is a preference for a network's nodes to attach to others that are similar in some way. Though the specific measure of similarity may vary, network theorists often examine assortativity in terms of a node's degree. The addition of this characteristic to network models more closely approximates the behaviors of many real world networks. Correlations between nodes of similar degree are often found in the mixing patterns of many observable networks. For instance, in social networks, nodes tend to be connected with other nodes with similar degree values. This tendency is referred to as assortative mixing, or ''assortativity''. On the other hand, technological and biological networks typically show disassortative mixing, or ''disassortativity'', as high degree nodes tend to attach to low degree nodes. Measurement Assortativity is often operationalized as a correlation between two nodes. However, there are several ways to capture such a correlat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robustness Of Complex Networks
Robustness, the ability to withstand failures and perturbations, is a critical attribute of many complex systems including complex networks. The study of robustness in complex networks is important for many fields. In ecology, robustness is an important attribute of ecosystems, and can give insight into the reaction to disturbances such as the extinction of species. For biologists, network robustness can help the study of diseases and mutations, and how to recover from some mutations. In economics, network robustness principles can help understanding of the stability and risks of banking systems. And in engineering, network robustness can help to evaluate the resilience of infrastructure networks such as the Internet or power grids. Percolation theory The focus of robustness in complex networks is the response of the network to the removal of nodes or links. The mathematical model of such a process can be thought of as an inverse percolation process. Percolation theory model ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NetworkX
NetworkX is a Python library for studying graphs and networks. NetworkX is free software released under the BSD-new license. Features * Classes for graphs and digraphs. * Conversion of graphs to and from several formats. * Ability to construct random graphs or construct them incrementally. * Ability to find subgraphs, cliques, k-cores. * Explore adjacency, degree, diameter, radius, center, betweenness, etc. * Draw networks in 2D and 3D. Suitability NetworkX is suitable for operation on large real-world graphs: e.g., graphs in excess of 10 million nodes and 100 million edges. Due to its dependence on a pure-Python "dictionary of dictionary" data structure, NetworkX is a reasonably efficient, very scalable, highly portable framework for network and social network analysis. Integration NetworkX is integrated into SageMath. See also * Social network analysis software * JGraph diagrams.net (previously draw.io) is a free and open source cross-platform graph drawin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Preferential Attachment
A preferential attachment process is any of a class of processes in which some quantity, typically some form of wealth or credit, is distributed among a number of individuals or objects according to how much they already have, so that those who are already wealthy receive more than those who are not. "Preferential attachment" is only the most recent of many names that have been given to such processes. They are also referred to under the names Yule process, cumulative advantage, the rich get richer, and the Matthew effect. They are also related to Gibrat's law. The principal reason for scientific interest in preferential attachment is that it can, under suitable circumstances, generate power law distributions. If preferential attachment is non-linear, measured distributions may deviate from a power law. These mechanisms may generate distributions which are approximately power law over transient periods. Definition A preferential attachment process is a stochastic urn process, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
