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Sparse Network
In network science, a sparse network has ''much fewer'' links than the possible maximum number of links within that network (the opposite is a dense network). The study of sparse networks is a relatively new area primarily stimulated by the study of real networks, such as social and computer networks. The notion of ''much fewer'' links is, of course, colloquial and informal. While a threshold for a particular network may be invented, there is no universal threshold that defines what ''much fewer'' actually means. As a result, there is no formal sense of sparsity for any finite network, despite widespread agreement that most empirical networks are indeed sparse. There is, however, a formal sense of sparsity in the case of infinite network models, determined by the behavior of the number of edges (M) and/or the average degree () as the number of nodes (N) goes to infinity. Definitions A simple unweighted network of size N is called sparse if the number of links M in it is much ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Network Science
Network science is an academic field which studies complex networks such as telecommunication networks, computer networks, biological networks, cognitive and semantic networks, and social networks, considering distinct elements or actors represented by ''nodes'' (or ''vertices'') and the connections between the elements or actors as ''links'' (or ''edges''). The field draws on theories and methods including graph theory from mathematics, statistical mechanics from physics, data mining and information visualization from computer science, inferential modeling from statistics, and social structure from sociology. The United States National Research Council defines network science as "the study of network representations of physical, biological, and social phenomena leading to predictive models of these phenomena." Background and history The study of networks has emerged in diverse disciplines as a means of analyzing complex relational data. The earliest known paper in this f ... [...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] |
Networks
Network, networking and networked may refer to: Science and technology * Network theory, the study of graphs as a representation of relations between discrete objects * Network science, an academic field that studies complex networks Mathematics * Networks, a graph with attributes studied in network theory ** Scale-free network, a network whose degree distribution follows a power law ** Small-world network, a mathematical graph in which most nodes are not neighbors, but have neighbors in common * Flow network, a directed graph where each edge has a capacity and each edge receives a flow Biology * Biological network, any network that applies to biological systems * Ecological network, a representation of interacting species in an ecosystem * Neural network, a network or circuit of neurons Technology and communication * Artificial neural network, a computing system inspired by animal brains * Broadcast network, radio stations, television stations, or other electronic media outlets ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adjacency Matrix
In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. In the special case of a finite simple graph, the adjacency matrix is a (0,1)-matrix with zeros on its diagonal. If the graph is undirected (i.e. all of its edges are bidirectional), the adjacency matrix is symmetric. The relationship between a graph and the eigenvalues and eigenvectors of its adjacency matrix is studied in spectral graph theory. The adjacency matrix of a graph should be distinguished from its incidence matrix, a different matrix representation whose elements indicate whether vertex–edge pairs are incident or not, and its degree matrix, which contains information about the degree of each vertex. Definition For a simple graph with vertex set , the adjacency matrix is a square matrix such that its element is one when there is an edge from vertex to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adjacency List
In graph theory and computer science, an adjacency list is a collection of unordered lists used to represent a finite graph. Each unordered list within an adjacency list describes the set of neighbors of a particular vertex in the graph. This is one of several commonly used representations of graphs for use in computer programs. Implementation details An adjacency list representation for a graph associates each vertex in the graph with the collection of its neighbouring vertices or edges. There are many variations of this basic idea, differing in the details of how they implement the association between vertices and collections, in how they implement the collections, in whether they include both vertices and edges or only vertices as first class objects, and in what kinds of objects are used to represent the vertices and edges. * An implementation suggested by Guido van Rossum uses a hash table to associate each vertex in a graph with an array of adjacent vertices. In this repre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Engineering
Computer engineering (CoE or CpE) is a branch of electrical engineering and computer science that integrates several fields of computer science and electronic engineering required to develop computer hardware and software. Computer engineers not only require training in electronic engineering, software design, and hardware-software integration, but also in software engineering. It uses the techniques and principles of electrical engineering and computer science, but also covers areas such as artificial intelligence (AI), robotics, computer networks, computer architecture and operating systems. Computer engineers are involved in many hardware and software aspects of computing, from the design of individual microcontrollers, microprocessors, personal computers, and supercomputers, to circuit design. This field of engineering not only focuses on how computer systems themselves work, yet it also demands them to integrate into the larger picture. Robots are one of the applicatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Network On A Chip
A network on a chip or network-on-chip (NoC or )This article uses the convention that "NoC" is pronounced . Therefore, it uses the convention "a" for the indefinite article corresponding to NoC ("a NoC"). Other sources may pronounce it as and therefore use "an NoC". is a network-based communications subsystem on an integrated circuit ("microchip"), most typically between modules in a system on a chip ( SoC). The modules on the IC are typically semiconductor IP cores schematizing various functions of the computer system, and are designed to be modular in the sense of network science. The network on chip is a router-based packet switching network between SoC modules. NoC technology applies the theory and methods of computer networking to on-chip communication and brings notable improvements over conventional bus and crossbar communication architectures. Networks-on-chip come in many network topologies, many of which are still experimental as of 2018. In 2000s researcher ... [...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] |
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] |
Computer Network
A computer network is a set of computers sharing resources located on or provided by network nodes. The computers use common communication protocols over digital interconnections to communicate with each other. These interconnections are made up of telecommunication network technologies, based on physically wired, optical, and wireless radio-frequency methods that may be arranged in a variety of network topologies. The nodes of a computer network can include personal computers, servers, networking hardware, or other specialised or general-purpose hosts. They are identified by network addresses, and may have hostnames. Hostnames serve as memorable labels for the nodes, rarely changed after initial assignment. Network addresses serve for locating and identifying the nodes by communication protocols such as the Internet Protocol. Computer networks may be classified by many criteria, including the transmission medium used to carry signals, bandwidth, communications pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sparse Graph
In mathematics, a dense graph is a graph in which the number of edges is close to the maximal number of edges (where every pair of vertices is connected by one edge). The opposite, a graph with only a few edges, is a sparse graph. The distinction of what constitutes a dense or sparse graph is ill-defined, and depends on context. The graph density of simple graphs is defined to be the ratio of the number of edges with respect to the maximum possible edges. For undirected simple graphs, the graph density is: :D = \frac = \frac For directed, simple graphs, the maximum possible edges is twice that of undirected graphs (as there are two directions to an edge) so the density is: :D = \frac = \frac where is the number of edges and is the number of vertices in the graph. The maximum number of edges for an undirected graph is = \frac2, so the maximal density is 1 (for complete graphs) and the minimal density is 0 . Upper density ''Upper density'' is an extension of the concept of g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Star (graph Theory)
In graph theory, a star is the complete bipartite graph a tree with one internal node and leaves (but no internal nodes and leaves when ). Alternatively, some authors define to be the tree of order with maximum diameter 2; in which case a star of has leaves. A star with 3 edges is called a claw. The star is edge-graceful when is even and not when is odd. It is an edge-transitive matchstick graph, and has diameter 2 (when ), girth ∞ (it has no cycles), chromatic index , and chromatic number 2 (when ). Additionally, the star has large automorphism group, namely, the symmetric group on letters. Stars may also be described as the only connected graphs in which at most one vertex has degree greater than one. Relation to other graph families Claws are notable in the definition of claw-free graphs, graphs that do not have any claw as an induced subgraph. They are also one of the exceptional cases of the Whitney graph isomorphism theorem: in general, graphs with isomor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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