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...

\mathbb {E} [\langle k\rangle ]=\mathbb {E} [k]=p(N-1)} . Degree distribution The degree distribution P ( k ) {\displaystyle P(k)} is a fundamental property...

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

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...

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

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

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

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

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

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

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

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

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...

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

scale-free networks where the degree distribution can be described by a pure power law. However, the degree distribution of most real life networks cannot...

particular interest of network science. It is characterized by its degree distribution following a power law. While the most widely known generative models...

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

show a scale-free (power law) degree distribution where the connectivity distribution P(k) ~ k−γ with k being the degree. This relationship can also be...

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

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

networks with scale-free topology where the in-and out-degree distribution is a power-law distribution: P ( K ) ∝ K − γ {\displaystyle P(K)\propto K^{-\gamma...

average ( n 2 ) p {\displaystyle {\tbinom {n}{2}}p} edges. The distribution of the degree of any particular vertex is binomial: P ( deg ⁡ ( v ) = k ) =...

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

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...

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

node degree distribution changes with the increasing connectivity. Different link densities in the complex networks have different node-degree distribution...

that a node's growth depends on its fitness and can calculate the degree distribution. The Bianconi–Barabási model is named after its inventors Ginestra...

the degree sequence from specific edge generation processes. This makes it suitable for analyzing networks with heterogeneous degree distributions, such...