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 subgraph of G induced by all vertices adjacent to v, i.e., the graph composed of the vertices adjacent to v and all edges connecting vertices adjacent to v. The neighbourhood is often denoted N_G (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.
Rook's graphIn graph theory, a rook's graph is an undirected graph that represents all legal moves of the rook chess piece on a chessboard. Each vertex of a rook's graph represents a square on a chessboard, and there is an edge between any two squares sharing a row (rank) or column (file), the squares that a rook can move between. These graphs can be constructed for chessboards of any rectangular shape.
Adjacency matrixIn 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.
CentralityIn graph theory and network analysis, indicators of centrality assign numbers or rankings to nodes within a graph corresponding to their network position. Applications include identifying the most influential person(s) in a social network, key infrastructure nodes in the Internet or urban networks, super-spreaders of disease, and brain networks. Centrality concepts were first developed in social network analysis, and many of the terms used to measure centrality reflect their sociological origin.
Network effectIn economics, a network effect (also called network externality or demand-side economies of scale) is the phenomenon by which the value or utility a user derives from a good or service depends on the number of users of compatible products. Network effects are typically positive, resulting in a given user deriving more value from a product as more users join the same network. The adoption of a product by an additional user can be broken into two effects: an increase in the value to all other users (total effect) and also the enhancement of other non-users' motivation for using the product (marginal effect).
World Wide WebThe World Wide Web (WWW), commonly known as the Web, is an information system enabling information to be shared over the Internet through simplified ways meant to appeal to users beyond IT specialists and hobbyists, as well as documents and other web resources to be accessed over the Internet according to specific rules, the Hypertext Transfer Protocol (HTTP). Documents and downloadable media are made available to the network through web servers and can be accessed by programs such as web browsers.
Climate as complex networksThe field of complex networks has emerged as an important area of science to generate novel insights into nature of complex systems The application of network theory to climate science is a young and emerging field. To identify and analyze patterns in global climate, scientists model climate data as complex networks. Unlike most real-world networks where nodes and edges are well defined, in climate networks, nodes are identified as the sites in a spatial grid of the underlying global climate data set, which can be represented at various resolutions.
Wireless networkA wireless network is a computer network that uses wireless data connections between network nodes. Wireless networking allows homes, telecommunications networks and business installations to avoid the costly process of introducing cables into a building, or as a connection between various equipment locations. Admin telecommunications networks are generally implemented and administered using radio communication. This implementation takes place at the physical level (layer) of the OSI model network structure.
Ring networkA ring network is a network topology in which each node connects to exactly two other nodes, forming a single continuous pathway for signals through each node – a ring. Data travels from node to node, with each node along the way handling every packet. Rings can be unidirectional, with all traffic travelling either clockwise or anticlockwise around the ring, or bidirectional (as in SONET/SDH). Because a unidirectional ring topology provides only one pathway between any two nodes, unidirectional ring networks may be disrupted by the failure of a single link.
Protein–protein interactionProtein–protein interactions (PPIs) are physical contacts of high specificity established between two or more protein molecules as a result of biochemical events steered by interactions that include electrostatic forces, hydrogen bonding and the hydrophobic effect. Many are physical contacts with molecular associations between chains that occur in a cell or in a living organism in a specific biomolecular context. Proteins rarely act alone as their functions tend to be regulated.
