Xulvi-Brunet–Sokolov algorithm Xulvi-Brunet and Sokolov's algorithm generates networks with chosen degree correlations. This method is based on link rewiring, in which the desired degree is governed by parameter ρ. By varying this single parameter it is possible to generate networks from random (when ρ = 0) to perfectly assortative or disassortative (when ρ = 1). This algorithm allows to keep network's degree distribution unchanged when changing the value of ρ.[1] Assortative model[edit] In assortative networks, well-connected nodes are likely to be connected to other highly connected nodes. The Xulvi-Brunet–Sokolov algorithm for this type of networks is the following. Disassortative model[edit] In disassortative networks, highly connected nodes tend to connect to less-well-connected nodes with larger probability than in uncorrelated networks. The Xulvi-Brunet and Sokolov's algorithm for this type of networks is similar to the one for assortative networks with one minor change. References[edit]
Network tomography Network tomography is the study of a network's internal characteristics using information derived from end point data. The word tomography is used to link the field, in concept, to other processes that infer the internal characteristics of an object from external observation, as is done in MRI or PET scanning (even though the term tomography strictly refers to imaging by slicing). The field is a recent development in electrical engineering and computer science, dating from 1996.[1] Network tomography seeks to map the path data takes through the Internet by examining information from “edge nodes,” the computers in which the data are originated and from which they are requested. The field is useful for engineers attempting to develop more efficient computer networks. Data derived from network tomography studies can be used to increase quality of service by limiting link packet loss and increasing routing optimization. Recent developments[edit] Loss tomography[edit] Delay tomography[edit]
Widest path problem Path-finding using high-weight graph edges A closely related problem, the minimax path problem or bottleneck shortest path problem asks for the path that minimizes the maximum weight of any of its edges. It has applications that include transportation planning.[7] Any algorithm for the widest path problem can be transformed into an algorithm for the minimax path problem, or vice versa, by reversing the sense of all the weight comparisons performed by the algorithm, or equivalently by replacing every edge weight by its negation. Undirected graphs[edit] In an undirected graph, a widest path may be found as the path between the two vertices in the maximum spanning tree of the graph, and a minimax path may be found as the path between the two vertices in the minimum spanning tree.[8][9][10] Fernández, Garfinkel & Arbiol (1998) use undirected bottleneck shortest paths in order to form composite aerial photographs that combine multiple images of overlapping areas. Directed graphs[edit]
Network science Academic field 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."[1] Background and history[edit] The study of networks has emerged in diverse disciplines as a means of analyzing complex relational data. Department of Defense initiatives[edit] . .
Weighted planar stochastic lattice Starting with a square, say of unit area, and dividing randomly at each step only one block, after picking it preferentially with respect to ares, into four smaller blocks creates weighted planar stochastic lattice (WPSL). Essentially it is a disordered planar lattice as its block size and their coordination number are random. Description[edit] Regular planar lattices like square lattices, triangular lattices, honeycomb lattices, etc., are the simplest example of the cellular structure in which every cell has exactly the same size and the same coordination number. The planar Voronoi diagram, on the other hand, has neither a fixed cell size nor a fixed coordination number. Its coordination number distribution is rather Poissonian in nature.[5] That is, the distribution is peaked about the mean where it is almost impossible to find cells which have significantly higher or fewer coordination number than the mean. Construction of WPSLs[edit] and . is the area of the th block. References[edit]
Networks in marketing Networks are crucial parts of any action taken in a marketplace.[1] Peter Drucker [2] even described the future economy as one of a society of networks. Companies embedded in such networks stand to gain a lot.[3][4] There are a number of different network models, which have distinct relevance to customers,[4] and marketing initiatives. A network in marketing can be formed either strategically (e.g. Business networking) or completely randomly (e.g. Referral economy). “Interdependent systems of organizations and relations that are involved in carrying out all of the production and marketing activities involved in creating and delivering value in the form of products and services to intermediate and final customers.” Achrol & Kotler [3] stated that networks are not accepting of traditional mechanisms, such as authority and control. Business and marketing networks differ in the amount of connectivity between agents. Networks in general[edit] History[edit] 1960s[edit] 1970s[edit] 1980s[edit]
Weighted network In a number of real-world networks, not all ties in a network have the same capacity. In fact, ties are often associated with weights that differentiate them in terms of their strength, intensity, or capacity[2][3] On the one hand, Mark Granovetter (1973)[4] argued that the strength of social relationships in social networks is a function of their duration, emotional intensity, intimacy, and exchange of services. On the other, for non-social networks, weights often refer to the function performed by ties, e.g., the carbon flow (mg/m2/day) between species in food webs,[5] the number of synapses and gap junctions in neural networks,[6] or the amount of traffic flowing along connections in transportation networks.[7] Example of a weighted network (weights can also be visualized by giving edges different widths) By recording the strength of ties,[8] a weighted network can be created (also known as a valued network). Measures for weighted networks[edit] See also[edit] References[edit]
Next-generation network services Next-generation network services is a jargon term with no specific meaning. The term is used, in some telecommunication communities, in a loose way to refer to services that have not traditionally been provided by telecommunication operators circuit switched networks. Services include VoIP, IPTV, presence-based applications, instant messaging and location-based services. All of these example services are deployed and used on the Internet or private IP networks and access is available to them from traditional circuit switched networks. Standards bodies and industry support forums[edit] Various industry forums have emerged to promote as well as standardize the evolving services of next generation networks. These forums generally host interoperability events in which multiple vendors show that services based on standards promoted by the forums can actually be deployed. Interoperability events[edit] References[edit]
Wang algebra From Wikipedia, the free encyclopedia Algebraic structure in network theory In algebra and network theory, a Wang algebra is a commutative algebra has two additional properties:(Rule i) For all elements x of , x + x = 0 (universal additive nilpotency of degree 1). , x⋅x = 0 (universal multiplicative nilpotency of degree 1).[1][2] History and applications[edit] According to Guo Jinhai, professor in the Institute for the History of Natural Sciences of the Chinese Academy of Sciences, Wang Ki Tung's pioneering method of analyzing electrical networks significantly promoted electrical engineering not only in China but in the rest of the world; the Wang algebra formulation is useful in electrical networks for solving problems involving topological methods, graph theory, and Hamiltonian cycles.[7] Wang Algebra and the Spanning Trees of a Graph[edit] The Wang Rules for Finding all Spanning Trees of a Graph G[8] References[edit]
Non-linear preferential attachment In network science, preferential attachment means that nodes of a network tend to connect to those nodes which have more links. If the network is growing and new nodes tend to connect to existing ones with linear probability in the degree of the existing nodes then preferential attachment leads to a scale-free network. If this probability is sub-linear then the network’s degree distribution is stretched exponential and hubs are much smaller than in a scale-free network. If this probability is super-linear then almost all nodes are connected to a few hubs. According to Kunegis, Blattner, and Moser several online networks follow a non-linear preferential attachment model. Communication networks and online contact networks are sub-linear while interaction networks are super-linear.[1] The co-author network among scientists also shows the signs of sub-linear preferential attachment.[2] Types of preferential attachment[edit] where α > 0. Sub-linear preferential attachment[edit]
Tribe (internet) The term tribe or digital tribe[1] is used as a slang term for an unofficial community of people who share a common interest, and usually who are loosely affiliated with each other through social media or other internet mechanisms. The term is related to "tribe," which traditionally refers to people closely associated in both geography and genealogy. The concept is closely related to social networking, and dates back to at least 2003, when tribe.net was launched. Cory Doctorow wrote a science fiction novel that expounds on this concept released in 2004 called Eastern Standard Tribe. Analysis and identification of tribes often relies heavily on algorithms and techniques from statistical physics, computational biology and network science[2] Communication between and within tribes of Twitter users clustered based on word usage. Each tribe has a campfire around which they gather. Cooperation e.g. However, some brands are building their own tribes around platforms outside of these.