the degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability distribution of these...

scale-free networks, meaning that they have power-law (or scale-free) degree distributions, while random graph models such as the Erdős–Rényi (ER) model and...

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...

for the formation of hubs. Formally, the degree distribution of ER graphs converges to a Poisson distribution, rather than a power law observed in many...

degree distribution follows a power law function. In some empirical examples this power-law fits the degree distribution well only in the high degree...

theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable...

regular nor purely random. Such features include a heavy tail in the degree distribution, a high clustering coefficient, assortativity or disassortativity...

which each subgraph has a vertex of degree at most k. Indegree, outdegree for digraphs Degree distribution Degree sequence for bipartite graphs Diestel...

consequently the degree distribution will be enriched at high degree values. This is known colloquially as a fat-tailed distribution. Graphs of very different...

The configuration model takes a degree sequence or degree distribution (which subsequently is used to generate a degree sequence) as the input, and produces...

tree-like random graphs with non-uniform degree distributions P ( k ) {\displaystyle P(k)} . The degree distribution does not define a graph uniquely. However...

networks is the clustering coefficient distribution, which decreases as the node degree increases. This distribution also follows a power law. The Barabási...

the distribution of the nodes' clustering coefficients: as other models would predict a constant clustering coefficient as a function of the degree of...

Student's t distribution (or simply the t distribution)   t ν   {\displaystyle \ t_{\nu }\ } is a continuous probability distribution that generalizes...

function corresponding to the excess degree distribution. So, for random Erdős–Rényi networks of average degree ⟨ k ⟩ {\displaystyle \langle k\rangle...

probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval [0, 1] or (0, 1) in...

power-law degree distribution to properly estimate it. However, sampling random friends incorporates more nodes from the tail of the degree distribution (i.e...

examples are the Rayleigh distribution (chi distribution with two degrees of freedom) and the Maxwell–Boltzmann distribution of the molecular speeds in...

undirected graph equals to the degree distribution vector if and only if the graph is regular, i.e., every vertex has the same degree. A generalization of PageRank...

Lorentz distribution (after Hendrik Lorentz), Cauchy–Lorentz distribution, Lorentz(ian) function, or Breit–Wigner distribution. The Cauchy distribution f (...

examination with computer experiments. At a given point of time, degree distribution u ( n ) {\displaystyle u(n)} , is the probability that a randomly...

theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in...

with the chi distribution with two degrees of freedom. The distribution is named after Lord Rayleigh (/ˈreɪli/). A Rayleigh distribution is often observed...

probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally...

gamma distribution is a versatile two-parameter family of continuous probability distributions. The exponential distribution, Erlang distribution, and...

notion of the degree distribution to the spectrum of graphlet degree distributions (GDDs) in the following way. The degree distribution measures the number...

g_{1}(z)} is the generating function corresponding to the excess degree distribution. In networks with low clustering, 0 < C ≪ 1 {\displaystyle 0<C\ll...

chi-squared distribution (also chi-square or χ 2 {\displaystyle \chi ^{2}} -distribution) with k {\displaystyle k} degrees of freedom is the distribution of a...

gradient network, the in-degree of a node i, ki (in) is the number of gradient edges pointing into i, and the in-degree distribution is R ( l ) = P { k i...

arbitrary degree distributions. In the configuration model, the degree of each vertex is pre-defined, rather than having a probability distribution from which...