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Network Topology Network topology Network topology is the arrangement of the various elements (links, nodes, etc.) of a communication network.[1][2] Network topology Network topology is the topological[3] structure of a network and may be depicted physically or logically. It is an application of graph theory[4] wherein communicating devices are modeled as nodes and the connections between the devices are modeled as links or lines between the nodes. Physical topology is the placement of the various components of a network (e.g., device location and cable installation), while logical topology illustrates how data flows within a network. Distances between nodes, physical interconnections, transmission rates, or signal types may differ between two different networks, yet their topologies may be identical. A network’s physical topology is a particular concern of the physical layer of the OSI model [...More...] 


Transport Topology Rapid transit Rapid transit or mass rapid transit, also known as heavy rail, metro, subway, tube, or underground, is a type of highcapacity public transport generally found in urban areas.[1][2][3] Unlike buses or trams, rapid transit systems are electric railways that operate on an exclusive rightofway, which cannot be accessed by pedestrians or other vehicles of any sort,[4] and which is often grade separated in tunnels or on elevated railways. Modern services on rapid transit systems are provided on designated lines between stations typically using electric multiple units on rail tracks, although some systems use guided rubber tires, magnetic levitation, or monorail.[citation needed] The stations typically have high platforms, without steps inside the trains, requiring custommade trains in order to minimize gaps between train and platform. They are typically integrated with other public transport and often operated by the same public transport authorities [...More...] 


Cycle (graph Theory) In graph theory, a cycle is a path of edges and vertices wherein a vertex is reachable from itself. There are several different types of cycles, principally a closed walk and a simple cycle; also, e.g., an element of the cycle space of the graph.Contents1 Definitions 2 Chordless cycles 3 Cycle space 4 Cycle detection 5 Covering graphs by cycles 6 Graph classes defined by cycles 7 See also 8 ReferencesDefinitions[edit] A closed walk consists of a sequence of vertices starting and ending at the same vertex, with each two consecutive vertices in the sequence adjacent to each other in the graph. In a directed graph, each edge must be traversed by the walk consistently with its direction: the edge must be oriented from the earlier of two consecutive vertices to the later of the two vertices in the sequence [...More...] 


Artificial Neural Network Artificial neural networks (ANNs) or connectionist systems are computing systems vaguely inspired by the biological neural networks that constitute animal brains.[1] Such systems "learn" (i.e. progressively improve performance on) tasks by considering examples, generally without taskspecific programming. For example, in image recognition, they might learn to identify images that contain cats by analyzing example images that have been manually labeled as "cat" or "no cat" and using the results to identify cats in other images. They do this without any a priori knowledge about cats, e.g., that they have fur, tails, whiskers and catlike faces. Instead, they evolve their own set of relevant characteristics from the learning material that they process. An ANN is based on a collection of connected units or nodes called artificial neurons (a simplified version of biological neurons in an animal brain) [...More...] 


Interdependent Networks Interdependence is the mutual reliance between two or more groups. This concept differs from the reliance in a dependent relationship, where some members are dependent and some are not. There can be various degrees of interdependence. In an interdependent relationship, participants may be emotionally, economically, ecologically or morally reliant on and responsible to each other. An interdependent relationship can arise between two or more cooperative autonomous participants (e.g. a coop) [...More...] 


Semantic Network A semantic network, or frame network is a knowledge base that represents semantic relations between concepts in a network. This is often used as a form of knowledge representation. It is a directed or undirected graph consisting of vertices, which represent concepts, and edges, which represent semantic relations between concepts.[1] Typical standardized semantic networks are expressed as semantic triples. Semantic networks are in use in various Natural Language Processing applications.Contents1 History 2 Basics of semantic networks 3 Examples3.1 Semantic Net in Lisp 3.2 WordNet 3.3 Other examples4 Software tools 5 See also5.1 Other examples6 References 7 Further reading 8 External linksHistory[edit]Example of a semantic network"Semantic Nets" were first invented for computers by Richard H. Richens of the Cambridge Language Research Unit in 1956 as an "interlingua" for machine translation of natural languages.[2] They were independently developed by Robert F [...More...] 


Spatial Network A spatial network (sometimes also geometric graph) is a graph in which the vertices or edges are spatial elements associated with geometric objects, i.e. the nodes are located in a space equipped with a certain metric.[1][2] The simplest mathematical realization is a lattice or a random geometric graph, where nodes are distributed uniformly at random over a twodimensional plane; a pair of nodes are connected if the Euclidean distance Euclidean distance is smaller than a given neighborhood radius. Transportation and mobility networks, Internet, mobile phone networks, power grids, social and contact networks and neural networks are all examples where the underlying space is relevant and where the graph's topology alone does not contain all the information [...More...] 


Dependency Network The dependency network approach provides a system level analysis of the activity and topology of directed networks. The approach extracts causal topological relations between the network's nodes (when the network structure is analyzed), and provides an important step towards inference of causal activity relations between the network nodes (when analyzing the network activity). This methodology has originally been introduced for the study of financial data,[1][2] it has been extended and applied to other systems, such as the immune system,[3] and semantic networks.[4] In the case of network activity, the analysis is based on partial correlations,[5][6][7][8][9] which are becoming ever more widely used to investigate complex systems. In simple words, the partial (or residual) correlation is a measure of the effect (or contribution) of a given node, say j, on the correlations between another pair of nodes, say i and k [...More...] 


Flow Network In graph theory, a flow network (also known as a transportation network) is a directed graph where each edge has a capacity and each edge receives a flow. The amount of flow on an edge cannot exceed the capacity of the edge. Often in operations research, a directed graph is called a network, the vertices are called nodes and the edges are called arcs. A flow must satisfy the restriction that the amount of flow into a node equals the amount of flow out of it, unless it is a source, which has only outgoing flow, or sink, which has only incoming flow [...More...] 


Clique (graph Theory) In the mathematical area of graph theory, a clique (/ˈkliːk/ or /ˈklɪk/) is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are adjacent; that is, its induced subgraph is complete. Cliques are one of the basic concepts of graph theory and are used in many other mathematical problems and constructions on graphs. Cliques have also been studied in computer science: the task of finding whether there is a clique of a given size in a graph (the clique problem) is NPcomplete, but despite this hardness result, many algorithms for finding cliques have been studied. Although the study of complete subgraphs goes back at least to the graphtheoretic reformulation of Ramsey theory by Erdős & Szekeres (1935),[1] the term clique comes from Luce & Perry (1949), who used complete subgraphs in social networks to model cliques of people; that is, groups of people all of whom know each other [...More...] 


Connected Component (graph Theory) In graph theory, a connected component (or just component) of an undirected graph is a subgraph in which any two vertices are connected to each other by paths, and which is connected to no additional vertices in the supergraph. For example, the graph shown in the illustration has three connected components. A vertex with no incident edges is itself a connected component. A graph that is itself connected has exactly one connected component, consisting of the whole graph.Contents1 An equivalence relation 2 The number of connected components 3 Algorithms 4 See also 5 References 6 External linksAn equivalence relation[edit] An alternative way to define connected components involves the equivalence classes of an equivalence relation that is defined on the vertices of the graph. In an undirected graph, a vertex v is reachable from a vertex u if there is a path from u to v [...More...] 


Cut (graph Theory) In graph theory, a cut is a partition of the vertices of a graph into two disjoint subsets. Any cut determines a cutset, the set of edges that have one endpoint in each subset of the partition. These edges are said to cross the cut. In a connected graph, each cutset determines a unique cut, and in some cases cuts are identified with their cutsets rather than with their vertex partitions. In a flow network, an s–t cut is a cut that requires the source and the sink to be in different subsets, and its cutset only consists of edges going from the source's side to the sink's side [...More...] 


Graph (abstract Data Type) In computer science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from mathematics, specifically the field of graph theory. A graph data structure consists of a finite (and possibly mutable) set of vertices or nodes or points, together with a set of unordered pairs of these vertices for an undirected graph or a set of ordered pairs for a directed graph. These pairs are known as edges, arcs, or lines for an undirected graph and as arrows, directed edges, directed arcs, or directed lines for a directed graph [...More...] 


Transport Network A transport network, or transportation network is a realisation of a spatial network, describing a structure which permits either vehicular movement or flow of some commodity.[1][2] Examples are network of roads and streets, railways, pipes, aqueducts, and power lines. One can distinguish land, sea and air transportation networks. Methods[edit] Transport network Transport network analysis is used to determine the flow of vehicles (or people) through a transport network, typically using mathematical graph theory. It may combine different modes of transport, for example, walking and car, to model multimodal journeys. Transport network analysis falls within the field of transport engineering. References[edit]^ M. Barthelemy, "Spatial Networks", Physics Reports 499:1101 (2011) ( https://arxiv.org/abs/1010.0302 ). ^ Boeing, G. (2017). "OSMnx: New Methods for Acquiring, Constructing, Analyzing, and Visualizing Complex Street Networks" [...More...] 


Edge (graph Theory) This is a glossary of graph theory terms. Graph theory Graph theory is the study of graphs, systems of nodes or vertices connected in pairs by edges.Contents: !$@ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z See also ReferencesSymbols[edit]Square brackets [ ] G[S] is the induced subgraph of a graph G for vertex subset S. Prime symbol ' The prime symbol is often used to modify notation for graph invariants so that it applies to the line graph instead of the given graph. For instance, α(G) is the independence number of a graph; α′(G) is the matching number of the graph, which equals the independence number of its line graph [...More...] 


Loop (graph Theory) In graph theory, a loop (also called a selfloop 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 [...More...] 
