[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/en\/wiki40\/copying-network-models-wikipedia\/#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/en\/wiki40\/copying-network-models-wikipedia\/","headline":"Copying network models – Wikipedia","name":"Copying network models – Wikipedia","description":"Copying network models are network generation models that use a copying mechanism to form a network, by repeatedly duplicating and","datePublished":"2018-10-12","dateModified":"2018-10-12","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/en\/wiki40\/author\/lordneo\/#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/en\/wiki40\/author\/lordneo\/","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/4e351d30ded09e7d285c21e836f116e14ad5ae28","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/4e351d30ded09e7d285c21e836f116e14ad5ae28","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/en\/wiki40\/copying-network-models-wikipedia\/","about":["Wiki"],"wordCount":5565,"articleBody":"Copying network models are network generation models that use a copying mechanism to form a network, by repeatedly duplicating and mutating existing nodes of the network. Such a network model has first been proposed in 1999 to explain the network of links between web pages, but since has been used to model biological and citation networks as well.Table of ContentsOrigins[edit]Description[edit]General model[edit]GNC model[edit]Walking model[edit]Biological networks[edit]Origins[edit]In 1999 Jon Kleinberg and 3 co-authors published an article to Computing and combinatorics attempting to construct a network model that explains patterns found in an analysis of the World Wide Web. The intuition behind the model was that when a user decides to build and publish her own web page, she encounters a list of links for her topic of interest on the web and ends up copying this collection, or many such collections to her own web page. This creating a new node in the network – the new page – and copying edges from already existing nodes in some fashion.They outlined a model very generally, but didn’t analyse the predictions of an exact model in detail, mostly due to computational limitations, but suggested that copying nodes randomly is a simple, model worthy mechanism for creating Zipfian distribution networks.[1]This paper since, has been cited over 1200 times, which is a number comparable to significant papers contributing to network science, like the one describing the Erd\u0151s\u2013R\u00e9nyi model (about 8300) and includes notable network science books like Mark Newman’s.[2]Description[edit]General model[edit]To understand a general model, take a basic network growth model, which is characterized by four stochastic processes. Creation processes Cv{displaystyle C_{v}} and Ce{displaystyle C_{e}} for node- and edge-creation, and deletion processes Dv{displaystyle D_{v}} and De{displaystyle D_{e}} for node- and edge-deletion.Take a discrete time timeframe, where Cv{displaystyle C_{v}} consists of simply at each step, creating a node with probability ac(t){displaystyle a_{c}(t)}, and similarly Dv{displaystyle D_{v}} is deleting a node with probability ad(t). Consequently, this also means De{displaystyle D_{e}} includes removing all edges that belonged to a node that was removed.Ce{displaystyle C_{e}} is where the essence of the copying model is. In the original article, they characterize Ce{displaystyle C_{e}} with a probability distribution, that determines a node v{displaystyle v} to add edges out of, and a number of edges k{displaystyle k} that will be added. And with probability \u03b2{displaystyle beta } that the k edges are either copied or added randomly. With probability \u03b2{displaystyle beta }, all k{displaystyle k} edges from v are drawn to nodes chosen independently and uniformly at random. With probability (1\u2212\u03b2){displaystyle (1-beta )}, the k edges are copied from a randomly chosen node u{displaystyle u}. Meaning that k{displaystyle k} neighbours of u{displaystyle u} become neighbours of v{displaystyle v}. If u{displaystyle u} has a degree higher than k{displaystyle k}, k{displaystyle k} edges are selected randomly and if it has a lower degree l={displaystyle gamma =} 2\u2212a1\u2212a{displaystyle {frac {2-a}{1-a}}} where a{displaystyle a} is the ratio of number of the randomly added edges to the number of the copied edges. [3] So with a ratio between zero and 0.5 a power law distribution with an exponent of 2"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/en\/wiki40\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/en\/wiki40\/copying-network-models-wikipedia\/#breadcrumbitem","name":"Copying network models – Wikipedia"}}]}]