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Network Topology
NETWORK TOPOLOGY is the arrangement of the various elements (links , nodes , etc.) of a computer network . Essentially, it is the topological structure of a network and may be depicted physically or logically. Physical topology is the placement of the various components of a network, including device location and cable installation, while logical topology illustrates how data flows within a network, regardless of its physical design. Distances between nodes, physical interconnections, transmission rates , or signal types may differ between two networks, yet their topologies may be identical. An example is a local area network (LAN). Any given node in the LAN has one or more physical links to other devices in the network; graphically mapping these links results in a geometric shape that can be used to describe the physical topology of the network. Conversely, mapping the data flow between the components determines the logical topology of the network
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Semantic Network
A SEMANTIC NETWORK, or FRAME NETWORK, is a network that represents semantic relations between concepts . 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. Typical standardized semantic networks are expressed as semantic triples . CONTENTS * 1 History * 2 Basics of semantic networks * 3 Examples * 3.1 Semantic Net in Lisp * 3.2 WordNet
WordNet
* 3.3 Other examples * 4 Software tools * 5 See also * 5.1 Other examples * 6 References * 7 Further reading * 8 External links HISTORY 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 . They were independently developed by Robert F
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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 . The simplest mathematical realization is a lattice or a random geometric graph , where nodes are distributed uniformly at random over a two-dimensional plane; a pair of nodes are connected if the Euclidean distance is smaller than a given neighborhood radius. Transportation and mobility networks , Internet
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. Characterizing and understanding the structure, resilience and the evolution of spatial networks is crucial for many different fields ranging from urbanism to epidemiology
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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, it has been extended and applied to other systems, such as the immune system , and semantic networks . In the case of network activity, the analysis is based on partial correlations , 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
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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. A network can be used to model traffic in a road system, circulation with demands, fluids in pipes, currents in an electrical circuit, or anything similar in which something travels through a network of nodes
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Interdependent Networks
The study of INTERDEPENDENT NETWORKS is a subfield of network science dealing with phenomena caused by the interactions between complex networks . Though there may be a wide variety of interactions between networks, dependency focuses on the scenario in which the nodes in one network require support from nodes in another network. CONTENTS * 1 Motivation for the model * 2 Dependency links * 3 Percolation properties and phase transitions * 4 Dynamics of cascading failure * 4.1 Effect of network topology * 5 Localized attacks * 6 Recovery of nodes and links * 7 Comparison to many-particle systems in physics * 8 Reinforced Nodes * 9 Examples * 10 See also * 11 References MOTIVATION FOR THE MODELIn nature, networks rarely appear in isolation. They are typically elements in larger systems and can have non-trivial effects on one and other. For example, infrastructure networks exhibit interdependency to a large degree
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Artificial Neural Network
ARTIFICIAL NEURAL NETWORKS (ANNS) or CONNECTIONIST SYSTEMS are computing systems inspired by the biological neural networks that constitute animal brains. Such systems learn (progressively improve performance) to do tasks by considering examples, generally without task-specific 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 analytic results to identify cats in other images. They have found most use in applications difficult to express in a traditional computer algorithm using rule-based programming . An ANN is based on a collection of connected units called artificial neurons , (analogous to axons in a biological brain ). Each connection (synapse ) between neurons can transmit a signal to another neuron. The receiving (postsynaptic) neuron can process the signal(s) and then signal downstream neurons connected to it
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Incidence List
In graph theory and computer science , an ADJACENCY LIST is a collection of unordered lists used to represent a finite graph . Each list describes the set of neighbors of a vertex in the graph. This is one of several commonly used representations of graphs for use in computer programs
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Transport Topology
RAPID TRANSIT, also known as HEAVY RAIL, METRO, SUBWAY, TUBE, or UNDERGROUND, is a type of high-capacity public transport generally found in urban areas . Unlike buses or trams , rapid transit systems are electric railways that operate on an exclusive right-of-way , which cannot be accessed by pedestrians or other vehicles of any sort, 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 . The stations typically have high platforms, without steps inside the trains, requiring custom-made 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
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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 . Examples are network of roads and streets , railways, pipes, aqueducts, and power lines. One can distinguish land, sea and air transportation networks. METHODS 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 multi-modal journeys. Transport network analysis falls within the field of transport engineering . REFERENCES * ^ M
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Scientific Collaboration Network
SCIENTIFIC COLLABORATION NETWORK is a social network where nodes are scientists and links are co-authorships as the latter is one of the most well documented forms of scientific collaboration . It is an undirected, scale-free network where the degree distribution follows a power law with an exponential cutoff – most authors are sparsely connected while a few authors are intensively connected. The network has an assortative nature – hubs tend to link to other hubs and low-degree nodes tend to link to low-degree nodes. Assortativity is not structural, meaning that it is not a consequence of the degree distribution, but it is generated by some process that governs the network’s evolution. CONTENTS * 1 Study by Mark Newman * 2 Modeling frameworks * 2.1 Preferential attachment models for evolving networks * 3 References STUDY BY MARK NEWMANA detailed reconstruction of an actual collaboration was made by Mark Newman
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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 NP-complete
NP-complete
, 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 graph-theoretic reformulation of Ramsey theory by Erdős & Szekeres (1935) , the term clique comes from Luce that is, groups of people all of whom know each other. Cliques have many other applications in the sciences and particularly in bioinformatics
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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. CONTENTS * 1 An equivalence relation * 2 The number of connected components * 3 Algorithms * 4 See also * 5 References * 6 External links AN EQUIVALENCE RELATIONAn 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
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Neighbourhood (graph Theory)
In graph theory , an ADJACENT VERTEX of a vertex v in a graph is a vertex that is connected to v by an edge . The NEIGHBOURHOOD of a vertex v in a graph G is the induced subgraph of G consisting of all vertices adjacent to v. For example, the image shows a graph of 6 vertices and 7 edges. Vertex 5 is adjacent to vertices 1, 2, and 4 but it is not adjacent to 3 and 6. The neighbourhood of vertex 5 is the graph with three vertices, 1, 2, and 4, and one edge connecting vertices 1 and 2. The neighbourhood is often denoted NG(v) or (when the graph is unambiguous) N(v). The same neighbourhood notation may also be used to refer to sets of adjacent vertices rather than the corresponding induced subgraphs. The neighbourhood described above does not include v itself, and is more specifically the OPEN NEIGHBOURHOOD of v; it is also possible to define a neighbourhood in which v itself is included, called the CLOSED NEIGHBOURHOOD and denoted by NG
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Path (graph Theory)
In graph theory , a PATH in a graph is a finite or infinite sequence of edges which connect a sequence of vertices which, by most definitions, are all distinct from one another. In a directed graph , a DIRECTED PATH (sometimes called DIPATH ) is again a sequence of edges (or arcs) which connect a sequence of vertices, but with the added restriction that the edges all be directed in the same direction. Paths are fundamental concepts of graph theory, described in the introductory sections of most graph theory texts. See e.g. Bondy and Murty (1976), Gibbons (1985), or Diestel (2005). Korte et al. (1990) cover more advanced algorithmic topics concerning paths in graphs. CONTENTS * 1 Definitions * 2 Examples * 3 Finding paths * 4 See also * 5 References DEFINITIONSA path is a trail in which all vertices (except possibly the first and last) are distinct. A trail is a walk in which all edges are distinct
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Vertex (graph Theory)
In 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
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