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- Giant_component abstract "In network theory, a giant component is a connected component of a given random graph that contains a constant fraction of the entire graph's vertices.Giant components are a prominent feature of the Erdős–Rényi model of random graphs, in which each possible edge connecting pairs of a given set of n vertices is present, independently of the other edges, with probability p. In this model, if for any constant , then with high probability all connected components of the graph have size O(log n), and there is no giant component. However, for there is with high probability a single giant component, with all other components having size O(log n). For , intermediate between these two possibilities, the number of vertices in the largest component of the graph is with high probability proportional to .Alternatively, if one adds randomly selected edges one at a time, starting with an empty graph, then it is not until approximately edges have been added that the graph contains a large component, and soon after that the component becomes giant. More precisely, when edges have been added, for values of close to but larger than , the size of the giant component is approximately . However, according to the coupon collector's problem, edges are needed in order to have high probability that the whole random graph is connected.A similar sharp threshold between parameters that lead to graphs with all components small and parameters that lead to a giant component also occurs in random graphs with non-uniform degree distributions.".
- Giant_component wikiPageID "2379792".
- Giant_component wikiPageRevisionID "544083742".
- Giant_component hasPhotoCollection Giant_component.
- Giant_component subject Category:Graph_connectivity.
- Giant_component subject Category:Random_graphs.
- Giant_component type Abstraction100002137.
- Giant_component type Communication100033020.
- Giant_component type Graph107000195.
- Giant_component type RandomGraphs.
- Giant_component type VisualCommunication106873252.
- Giant_component comment "In network theory, a giant component is a connected component of a given random graph that contains a constant fraction of the entire graph's vertices.Giant components are a prominent feature of the Erdős–Rényi model of random graphs, in which each possible edge connecting pairs of a given set of n vertices is present, independently of the other edges, with probability p.".
- Giant_component label "Giant component".
- Giant_component label "Гигантская компонента".
- Giant_component sameAs m.077tdq.
- Giant_component sameAs Q4137985.
- Giant_component sameAs Q4137985.
- Giant_component sameAs Giant_component.
- Giant_component wasDerivedFrom Giant_component?oldid=544083742.
- Giant_component isPrimaryTopicOf Giant_component.