Random recursive tree
In probability theory, a random recursive tree is a rooted tree chosen uniformly at random from the recursive trees with a given number of vertices.
Percolation threshold
The percolation threshold is a mathematical concept in percolation theory that describes the formation of long-range connectivity in random systems. Below the threshold a giant connected component doe
Lancichinetti–Fortunato–Radicchi benchmark
Lancichinetti–Fortunato–Radicchi benchmark is an algorithm that generates benchmark networks (artificial networks that resemble real-world networks). They have a priori known communities and are used
Soft configuration model
In applied mathematics, the soft configuration model (SCM) is a random graph model subject to the principle of maximum entropy under constraints on the expectation of the degree sequence of sampled gr
Barabási–Albert model
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
Autologistic actor attribute models
Autologistic actor attribute models (ALAAMs) are a family of statistical models used to model the occurrence of node attributes (individual-level outcomes) in network data. They are frequently used wi
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
Loop-erased random walk
In mathematics, loop-erased random walk is a model for a random simple path with important applications in combinatorics, physics and quantum field theory. It is intimately connected to the uniform sp
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 or the evolution of a random network. They are named after Hungari
Activity-driven model
In network science, the activity-driven model is a temporal network model in which each node has a randomly-assigned "activity potential", which governs how it links to other nodes over time. Each nod
Bianconi–Barabási model
The Bianconi–Barabási model is a model in network science that explains the growth of complex evolving networks. This model can explain that nodes with different characteristics acquire links at diffe
The Strange Logic of Random Graphs
The Strange Logic of Random Graphs is a book on zero-one laws for random graphs. It was written by Joel Spencer and published in 2001 by Springer-Verlag as volume 22 of their book series Algorithms an
Random tree
In mathematics and computer science, a random tree is a tree or arborescence that is formed by a stochastic process. Types of random trees include:
* Uniform spanning tree, a spanning tree of a given
Random graph
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 ge
Watts–Strogatz model
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. Wat
Random cluster model
In statistical mechanics, probability theory, graph theory, etc. the random cluster model is a random graph that generalizes and unifies the Ising model, Potts model, and percolation model. It is used
Random regular graph
A random r-regular graph is a graph selected from , which denotes the probability space of all r-regular graphs on vertices, where and is even. It is therefore a particular kind of random graph, but t
Percolation critical exponents
In the context of the physical and mathematical theory of percolation, a percolation transition is characterized by a set of universal critical exponents, which describe the fractal properties of the
Stochastic block model
The stochastic block model is a generative model for random graphs. This model tends to produce graphs containing communities, subsets of nodes characterized by being connected with one another with p
Giant component
In network theory, a giant component is a connected component of a given random graph that contains a finite fraction of the entire graph's vertices.
Random geometric graph
In graph theory, a random geometric graph (RGG) is the mathematically simplest spatial network, namely an undirected graph constructed by randomly placing N nodes in some metric space (according to a
Maximum-entropy random graph model
Maximum-entropy random graph models are random graph models used to study complex networks subject to the principle of maximum entropy under a set of structural constraints, which may be global, distr