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55 relations: Alfréd Rényi, Alireza Mashaghi, Almost surely, Arborescence (graph theory), Béla Bollobás, Bose–Einstein condensation (network theory), Brownian tree, Cavity method, Chromatic polynomial, Complex network, Connection (mathematics), Countable set, Dot product, Dual-phase evolution, Edgar Gilbert, Erdős–Rényi model, Exponential random graph models, Graph (discrete mathematics), Graph isomorphism, Graph theory, Greedy algorithm, Hamiltonian path, Interdependent networks, Lancichinetti–Fortunato–Radicchi benchmark, Loop-erased random walk, Mathematics, Network probability matrix, Network science, Percolation, Percolation theory, Probabilistic method, Probability distribution, Probability theory, Rado graph, Random binary tree, Random forest, Random minimum spanning tree, Random regular graph, Random tree, Random variable, Rapidly-exploring random tree, Regular graph, Scale-free network, Scientific collaboration network, Semilinear response, Shlomo Havlin, Siméon Denis Poisson, Social Networks (journal), Stochastic block model, Stochastic process, ..., Szemerédi regularity lemma, Treap, Tree (graph theory), Up to, Vector space. Expand index (5 more) »
Alfréd Rényi
Alfréd Rényi (20 March 1921 – 1 February 1970) was a Hungarian mathematician who made contributions in combinatorics, graph theory, number theory but mostly in probability theory.
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Alireza Mashaghi
Alireza Mashaghi is a biophysicist and medical scientist at Leiden University and Harvard Medical School.
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Almost surely
In probability theory, one says that an event happens almost surely (sometimes abbreviated as a.s.) if it happens with probability one.
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Arborescence (graph theory)
In graph theory, an arborescence is a directed graph in which, for a vertex u called the root and any other vertex v, there is exactly one directed path from u to v. An arborescence is thus the directed-graph form of a rooted tree, understood here as an undirected graph.
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Béla Bollobás
Béla Bollobás FRS (born 3 August 1943) is a Hungarian-born British mathematician who has worked in various areas of mathematics, including functional analysis, combinatorics, graph theory, and percolation.
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Bose–Einstein condensation (network theory)
Bose–Einstein condensation in networks is a phase transition observed in complex networks that can be described with the same mathematical model as that explaining Bose–Einstein condensation in physics.
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Brownian tree
A Brownian tree, whose name is derived from Robert Brown via Brownian motion, is a form of computer art that was briefly popular in the 1990s, when home computers started to have sufficient power to simulate Brownian motion.
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Cavity method
The cavity method is a mathematical method presented by M. Mezard, Giorgio Parisi and Miguel Angel Virasoro in 1985 to solve some mean field type models in statistical physics, specially adapted to disordered systems.
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Chromatic polynomial
The chromatic polynomial is a graph polynomial studied in algebraic graph theory, a branch of mathematics.
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Complex network
In the context of network theory, a complex network is a graph (network) with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often occur in graphs modelling of real systems.
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Connection (mathematics)
In geometry, the notion of a connection makes precise the idea of transporting data along a curve or family of curves in a parallel and consistent manner.
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Countable set
In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.
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Dot product
In mathematics, the dot product or scalar productThe term scalar product is often also used more generally to mean a symmetric bilinear form, for example for a pseudo-Euclidean space.
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Dual-phase evolution
Dual phase evolution (DPE) is a process that drives self-organization within complex adaptive systems.
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Edgar Gilbert
Edgar Nelson Gilbert (July 25, 1923 – June 15, 2013) was an American mathematician and coding theorist, a longtime researcher at Bell Laboratories whose accomplishments include the Gilbert–Varshamov bound in coding theory, the Gilbert–Elliott model of bursty errors in signal transmission, and the Erdős–Rényi model for random graphs.
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Erdős–Rényi model
In the mathematical field of graph theory, the Erdős–Rényi model is either of two closely related models for generating random graphs.
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Exponential random graph models
Exponential random graph models (ERGMs) are a family of statistical models for analyzing data about social and other networks.
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Graph (discrete mathematics)
In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".
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Graph isomorphism
In graph theory, an isomorphism of graphs G and H is a bijection between the vertex sets of G and H such that any two vertices u and v of G are adjacent in G if and only if ƒ(u) and ƒ(v) are adjacent in H. This kind of bijection is commonly described as "edge-preserving bijection", in accordance with the general notion of isomorphism being a structure-preserving bijection.
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Graph theory
In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
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Greedy algorithm
A greedy algorithm is an algorithmic paradigm that follows the problem solving heuristic of making the locally optimal choice at each stage with the intent of finding a global optimum.
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Hamiltonian path
In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once.
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Interdependent networks
The study of interdependent networks is a subfield of network science dealing with phenomena caused by the interactions between complex networks.
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Lancichinetti–Fortunato–Radicchi benchmark
Lancichinetti–Fortunato–Radicchi (LFR) benchmark is an algorithm that generates benchmark networks (artificial networks that resemble real-world networks).
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Loop-erased random walk
In mathematics, loop-erased random walk is a model for a random simple path with important applications in combinatorics and, in physics, quantum field theory.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Network probability matrix
The network probability matrix describes the probability structure of a network based on the historical presence or absence of edges in a network.
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Network science
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).
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Percolation
In physics, chemistry and materials science, percolation (from Latin percōlāre, "to filter" or "trickle through") refers to the movement and filtering of fluids through porous materials.
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Percolation theory
In statistical physics and mathematics, percolation theory describes the behaviour of connected clusters in a random graph.
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Probabilistic method
The probabilistic method is a nonconstructive method, primarily used in combinatorics and pioneered by Paul Erdős, for proving the existence of a prescribed kind of mathematical object.
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Probability distribution
In probability theory and statistics, a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.
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Probability theory
Probability theory is the branch of mathematics concerned with probability.
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Rado graph
In the mathematical field of graph theory, the Rado graph, Erdős–Rényi graph, or random graph is a countably infinite graph that can be constructed (with probability one) by choosing independently at random for each pair of its vertices whether to connect the vertices by an edge.
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Random binary tree
In computer science and probability theory, a random binary tree is a binary tree selected at random from some probability distribution on binary trees.
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Random forest
Random forests or random decision forests are an ensemble learning method for classification, regression and other tasks, that operate by constructing a multitude of decision trees at training time and outputting the class that is the mode of the classes (classification) or mean prediction (regression) of the individual trees.
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Random minimum spanning tree
In mathematics, a random minimum spanning tree may be formed by assigning random weights from some distribution to the edges of an undirected graph, and then constructing the minimum spanning tree of the graph.
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Random regular graph
A random r-regular graph is a graph selected from \mathcal_, which denotes the probability space of all ''r''-regular graphs on n vertices, where 3 ≤ r Béla Bollobás, Random Graphs, 2nd edition, Cambridge University Press (2001), section 2.4: Random Regular Graphs It is therefore a particular kind of random graph, but the regularity restriction significantly alters the properties that will hold, since most graphs are not regular.
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Random tree
In mathematics and computer science, a random tree is a tree or arborescence that is formed by a stochastic process.
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Random variable
In probability and statistics, a random variable, random quantity, aleatory variable, or stochastic variable is a variable whose possible values are outcomes of a random phenomenon.
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Rapidly-exploring random tree
A rapidly exploring random tree (RRT) is an algorithm designed to efficiently search nonconvex, high-dimensional spaces by randomly building a space-filling tree.
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Regular graph
In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency.
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Scale-free network
A scale-free network is a network whose degree distribution follows a power law, at least asymptotically.
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Scientific collaboration network
Scientific collaboration network is a social network where nodes are scientists and links are co-authorships as the latter is one of the most well documented forms of scientific collaboration.
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Semilinear response
Semi-linear response theory (SLRT) is an extension of linear response theory (LRT) for mesoscopic circumstances: LRT applies if the driven transitions are much weaker/slower than the environmental relaxation/dephasing effect, while SLRT assumes the opposite conditions.
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Shlomo Havlin
Shlomo Havlin (born July 21, 1942) is a Professor in the Department of Physics at Bar-Ilan University, Ramat-Gan, Israel.
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Siméon Denis Poisson
Baron Siméon Denis Poisson FRS FRSE (21 June 1781 – 25 April 1840) was a French mathematician, engineer, and physicist, who made several scientific advances.
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Social Networks (journal)
Social Networks is a quarterly peer-reviewed academic journal covering research on social network theory.
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Stochastic block model
The stochastic block model is a generative model for random graphs.
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Stochastic process
--> In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a collection of random variables.
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Szemerédi regularity lemma
In mathematics, the Szemerédi regularity lemma states that every large enough graph can be divided into subsets of about the same size so that the edges between different subsets behave almost randomly.
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Treap
In computer science, the treap and the randomized binary search tree are two closely related forms of binary search tree data structures that maintain a dynamic set of ordered keys and allow binary searches among the keys.
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Tree (graph theory)
In mathematics, and more specifically in graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path.
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Up to
In mathematics, the phrase up to appears in discussions about the elements of a set (say S), and the conditions under which subsets of those elements may be considered equivalent.
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Vector space
A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.
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Probabilistic graph theory, Pseudorandom graph, Random graph theory, Random graphs, Random network.
References
[1] https://en.wikipedia.org/wiki/Random_graph
