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Rich-club Coefficient
The rich-club coefficient is a metric on Graph (discrete mathematics), graphs and Complex network, 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, 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 Biological network#Protein–protein interaction networks, protein interaction networks. Definition Non-normalized form The rich-club coefficient was first introduced a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph (discrete Mathematics)
In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a Set (mathematics), set of objects where some pairs of the objects are in some sense "related". The objects are represented by 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. 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'', then this graph is directed, because owing mon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Internet Topology
World Wide Web topology is distinct from Internet The Internet (or internet) is the Global network, global system of interconnected computer networks that uses the Internet protocol suite (TCP/IP) to communicate between networks and devices. It is a internetworking, network of networks ... topology. While the former focuses on how web pages are interconnected through hyperlinks, the latter refers to the layout of network infrastructure like routers, ISPs, and backbone connections. The Jellyfish model of the World Wide Web topology represents the web as a core of highly connected nodes (web pages) surrounded by layers of less connected nodes. The Bow Tie model, on the other hand, divides the web into distinct zones: a strongly connected core, an 'IN' group leading into the core, an 'OUT' group leading out, and disconnected components. This model emphasizes the flow of hyperlinks between different parts of the web.. Models of web page topology Jellyfish Model The si ... [...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 Graph theory, graphing representation consists of a set of Vertex (graph theory), nodes connected by Glossary of graph theory, 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 1930s-1950s the study of random graphs were developed. During the mid 1990s, 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 medicine. In 2014, graph theoretical methods were used by Frank Emmert-Streib to an ... [...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] |
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 corr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robustness Of Complex Networks
Robustness is the property of being strong and healthy in constitution. When it is transposed into a system, it refers to the ability of tolerating perturbations that might affect the system's functional body. In the same line ''robustness'' can be defined as "the ability of a system to resist change without adapting its initial stable configuration". "Robustness in the small" refers to situations wherein perturbations are small in magnitude, which considers that the "small" magnitude hypothesis can be difficult to verify because "small" or "large" depends on the specific problem. Conversely, "Robustness in the large problem" refers to situations wherein no assumptions can be made about the magnitude of perturbations, which can either be small or large.C.Alippi: "Robustness Analysis" chapter in ''Intelligence for Embedded Systems.'' Springer, 2014, 283pp, . It has been discussed that robustness has two dimensions: resistance and avoidance.Durach, C.F. et al. (2015)Antecedents and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NetworkX
NetworkX is a Python (programming language), Python library for studying Graph (discrete mathematics), graphs and Network theory, networks. NetworkX is free software released under the BSD-new, BSD-new license. History NetworkX began development in 2002 by Aric A. Hagberg, Daniel A. Schult, and Pieter J. Swart.Aric A. Hagberg, Daniel A. Schult, Pieter J. SwartExploring Network Structure, Dynamics, and Function using NetworkX ''Proceedings of the 7th Python in Science conference (SciPy 2008)'', G. Varoquaux, T. Vaught, J. Millman (Eds.), pp. 11–15. It is supported by the National Nuclear Security Administration of the U.S. Department of Energy at Los Alamos National Laboratory. The package was crafted with the aim of creating tools to analyze data and intervention strategies for controlling the epidemic spread of disease, while also exploring the structure and dynamics of more general social, biological, and infrastructural systems. Inspired by Guido van Rossum's 1998 essay ... [...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 p ... [...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] |
