Hierarchical closeness Hierarchical closeness (HC) is a structural centrality measure used in network theory or graph theory. It is extended from closeness centrality to rank how centrally located a node is in a directed network. While the original closeness centrality of a directed network considers the most important node to be that with the least total distance from all other nodes, hierarchical closeness evaluates the most important node as the one which reaches the most nodes by the shortest paths. where is the set of nodes and is the set of interactions, hierarchical closeness of a node called was proposed by Tran and Kwon[1] as follows: where: is the reachability of a node defined by a path from to , and is the normalized form of original closeness (Sabidussi, 1966).[2] It can use a variant definition of closeness[3] as follows: where is the distance of the shortest path, if any, from to ; otherwise, is specified as an infinite value. In the formula, represents the number of nodes in . , then because is . .
Holarchy Different meanings[edit] David Spangler uses the term in a different meaning: "In a hierarchy, participants can be compared and evaluated on the basis of position, rank, relative power, seniority, and the like. But in a holarchy each person’s value comes from his or her individuality and uniqueness and the capacity to engage and interact with others to make the fruits of that uniqueness available. In multiagent systems[edit] Multiagent systems are systems composed of autonomous software entities. Janus Multiagent Platform is a software platform able to execute holarchies of agents. See also[edit] References[edit] External links[edit] Brief essay on holarchies
Holon (philosophy) A holon (Greek: ὅλον, holon neuter form of ὅλος, holos "whole") is something that is simultaneously a whole and a part. The word was coined by Arthur Koestler in his book The Ghost in the Machine (1967, p. 48). Koestler was compelled by two observations in proposing the notion of the holon. The first observation was influenced by Nobel Prize winner Herbert A. Simon's parable of the two watchmakers, wherein Simon concludes that complex systems will evolve from simple systems much more rapidly if there are stable intermediate forms present in that evolutionary process than if they are not present.[1] The second observation was made by Koestler himself in his analysis of hierarchies and stable intermediate forms in both living organisms and social organizations. He concluded that, although it is easy to identify sub-wholes or parts, wholes and parts in an absolute sense do not exist anywhere. A hierarchy of holons is called a holarchy. Jump up ^ Simon, Herbert A. (1969).
Graphlets Graphlets in mathematics are induced subgraph isomorphism classes in a graph,[1][2] i.e. two graphlet occurrences are isomorphic, whereas two graphlets are non-isomorphic. Graphlets differ from network motifs in a statistical sense, network motifs are defined as over- or under-represented graphlets with respect to some random graph null model. Graphlet-based network properties[edit] Relative graphlet frequency distance[edit] RGF-distance compares the frequencies of the appearance of all 3-5-node graphlets in two networks.[1] Let Ni(G) be the number of graphlets of type ) in network G, and let be the total number of graphlets of G. , where . Graphlet degree distribution agreement[edit] GDD-agreement generalizes the notion of the degree distribution to the spectrum of graphlet degree distributions (GDDs) in the following way.[2] The degree distribution measures the number of nodes of degree k in graph G, i.e., the number of nodes "touching" k edges, for each value of k. , for , and . .
Homoarchy Homoarchy is "the relation of elements to one another when they are rigidly ranked one way only, and thus possess no (or not more than very limited) potential for being unranked or ranked in another or a number of different ways at least without cardinal reshaping of the whole socio-political order."[1] Homoarchy and Heterarchy[edit] This notion is coupled with the one of heterarchy, defined by Crumley as "the relation of elements to one another when they are unranked or when they possess the potential for being ranked in a number of different ways". Homoarchy and Hierarchy[edit] Homoarchy must not be identified with hierarchy (as well as heterarchy must not be confused with egalitarianism in the proper meaning of the word). Notes[edit] ^ (Bondarenko D.M. Bibliography[edit] Bondarenko D.M., Grinin L.E., Korotayev A.V. 2002. See also[edit] Tree structure
Hydraulic power network The pumping station and hydraulic accumulator at Bristol Docks The idea of a public hydraulic power network was suggested by Joseph Bramah in a patent obtained in 1812. William Armstrong began installing systems in England from the 1840s, using low-pressure water, but a breakthrough occurred in 1850 with the introduction of the hydraulic accumulator, which allowed much higher pressures to be used. The first public network, supplying many companies, was constructed in Kingston upon Hull, England. The Hull Hydraulic Power Company began operation in 1877, with Edward B. Ellington as its engineer. History[edit] Joseph Bramah, an inventor and locksmith living in London, registered a patent at the London Patent Office on 29 April 1812, which was principally about a provision of a public water supply network, but included a secondary concept for the provision of a high-pressure water main, which would enable workshops to operate machinery. Public power in the United Kingdom[edit] London[edit]
GRAph ALigner (GRAAL) and by producing an alignment that consists of a set of ordered pairs , where is a node in When aligning two graphs , GRAAL first computes costs of aligning each node in G with each node in be the degree of a node in network , let be the maximum degree of nodes in , and let be a parameter in [0, 1] that controls the contribution of the node signature similarity to the cost function (that is, is the parameter that controls the contribution of node degrees to the cost function), then the cost of aligning nodes is computed as: . corresponds to a pair of topologically identical nodes , while a cost close to corresponds to a pair of topologically different nodes. GRAAL chooses as the initial seed a pair of nodes , that have the smallest cost. . around node is the set of nodes that are at distance from , where the distance is the length of the shortest path from to . that are not already aligned and that can be aligned with the minimal cost. have been aligned, some nodes in both networks may remain unaligned. for , i.e
Hyperbolic geometric graph Mathematical formulation[edit] ) and an edge set E constructed by considering the nodes as points placed onto a 2-dimensional hyperbolic space of constant negative Gaussian curvature, and cut-off radius , i.e. the radius of the Poincaré disk which can be visualized using a hyperboloid model. has hyperbolic polar coordinates with and The hyperbolic law of cosines allows to measure the distance between two points The angle In the simplest case, an edge is established iff (if and only if) two nodes are within a certain neighborhood radius , this corresponds to an influence threshold. Connectivity decay function[edit] In general, a link will be established with a probability depending on the distance . represents the probability of assigning an edge to a pair of nodes at distance . Generating hyperbolic geometric graphs[edit] Krioukov et al.[2] describe how to generate hyperbolic geometric graphs with uniformly random node distribution (as well as generalized versions) on a disk of radius in . exist iff . for
Icelandic Arctic Cooperation Network Icelandic Arctic Cooperation Network The Icelandic Arctic Cooperation Network (IACN) is a non-governmental organization in Iceland creating stronger linkages through inclusive multi-stakeholder membership and network, for the facilitation of cooperation concerning the Arctic region.[1] Recent additional members include the Centre for Gender Equality; the Fisheries Science Centre at the University of Akureyri; the Husavik Academic Centre; Arctic Services; the Icelandic Met Office; the Marine Research Institute; the Icelandic Maritime Administration; the University Centre of the Westfjords; and the Greenland Centre, also in the Westfjords of Iceland. IACN's first director is Embla Eir Oddsdóttir.[3] The Icelandic Arctic Cooperation Network is one of four founders of the Icelandic-Arctic Chamber of Commerce. The other three are the Ministry for Foreign Affairs, Iceland; The Icelandic Chamber of Commerce; and the Federation of Icelandic Industries.[4]
Gradient network Definition[edit] Transport takes place on a fixed network called the substrate graph. It has N nodes, and the set of edges . Let us also consider a scalar field, h = {h0, .., hN−1} defined on the set of nodes V, so that every node i has a scalar value hi associated to it. Gradient ∇hi on a network: ∇hi (i, μ(i)) i.e. the directed edge from i to μ(i), where μ(i) ∈ Si(1) ∪ {i}, and hμ has the maximum value in Gradient network : ∇ where F is the set of gradient edges on G. In general, the scalar field depends on time, due to the flow, external sources and sinks on the network. will be dynamic.[3] Motivation and history[edit] The concept of a gradient network was first introduced by Toroczkai and Bassler (2004).[4][5] Moreover, this flow is often generated or influenced by local gradients of a scalar. Recent research[which?] In-degree distribution of gradient networks[edit] In the limit and , the degree distribution becomes the power law The congestion on networks[edit] means no congestion, and
Individual mobility Data[edit] In recent years, there has been a surge in large data sets available on human movements. These data sets are usually obtained from cell phone or GPS data, with varying degrees of accuracy. For example, cell phone data is usually recorded whenever a call or a text message has been made or received by the user, and contains the location of the tower that the phone has connected to as well as the time stamp.[13] In urban areas, user and the telecommunication tower might be only a few hundred meters away from each other, while in rural areas this distance might well be in region of a few kilometers. Researchers have been able to extract very detailed information about the people whose data are made available to public. Characteristics[edit] At the large scale, when the behaviour is modelled over a period of relatively long duration (e.g. more than one day), human mobility can be described by three major components: where . , will choose his trip distance according to See also[edit]
Global production network Global production network Global Production Networks[edit] A global production network is one whose interconnected nodes and links extend spatially across national boundaries and, in so doing, integrates parts of disparate national and subnational territories".[1] GPN frameworks combines the insights from the global value chain analysis, actor–network theory and literature on Varieties of Capitalism. GPN provides a relational framework that aims to encompass all the relevant actors in the production systems. GPN framework provides analytical platform that relates sub-national regional development[2] with clustering dynamics.[3] Historical development of concept[edit] In 1990s the concept of value chain gained its credit among economists and business scholars. sets of interorganizational networks clustered around one commodity or product, linking households, enterprises, and states to one another within the world-economy. Insights from the analysis of production networks[edit]