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In the mathematical field of graph theory, the Erdős–Rényi model refers to one of two closely related models for generating random graphs or the evolution of a random network. These models are named after Hungarian mathematicians Paul Erdős and Alfréd Rényi, who introduced one of the models in 1959. [ 1][ 2] Edgar Gilbert introduced the ...
t. e. In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability distribution, or by a random process which generates them. [ 1][ 2] The theory of random graphs lies at the intersection between graph theory and probability theory.
Evolution of a random network is a dynamical process in random networks, usually leading to emergence of giant components, accompanied with striking consequences on the network topology . To quantify this process, there is a need of inspection on how the size of the largest connected cluster within the network, , varies with the average degree ...
Network science. The Barabási–Albert (BA) model is an algorithm for generating random scale-free networks using a preferential attachment mechanism. Several natural and human-made systems, including the Internet, the World Wide Web, citation networks, and some social networks are thought to be approximately scale-free and certainly contain ...
Random neural network. The random neural network ( RNN) [ 1] is a mathematical representation of an interconnected network of neurons or cells which exchange spiking signals. It was invented by Erol Gelenbe and is linked to the G-network model of queueing networks as well as to Gene Regulatory Network models.
A scale-free network is a network whose degree distribution follows a power law, at least asymptotically. That is, the fraction P ( k) of nodes in the network having k connections to other nodes goes for large values of k as. where is a parameter whose value is typically in the range (wherein the second moment ( scale parameter) of is infinite ...
Network science. Watts–Strogatz small-world model generated by igraph and visualized by Cytoscape 2.5. 100 nodes. The Watts–Strogatz model is a random graph generation model that produces graphs with small-world properties, including short average path lengths and high clustering. It was proposed by Duncan J. Watts and Steven Strogatz in ...
Degree sequence and different network realizations in the configuration model [1] In network science, the configuration model is a method for generating random networks from a given degree sequence. It is widely used as a reference model for real-life social networks, because it allows the modeler to incorporate arbitrary degree distributions.