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第266行： − − === Erdős–Rényi random graph model === − [[File:ER model.svg|thumb|This [[Erdős–Rényi model]] is generated with {{math|<VAR>N</VAR> {{=}} 4}} nodes. For each edge in the complete graph formed by all {{mvar|N}} nodes, a random number is generated and compared to a given probability. If the random number is less than {{mvar|p}}, an edge is formed on the model.]] − The '''[[Erdős–Rényi model]]''', named for [[Paul Erdős]] and [[Alfréd Rényi]], is used for generating [[random graph]]s in which edges are set between nodes with equal probabilities. It can be used in the [[probabilistic method]] to prove the existence of graphs satisfying various properties, or to provide a rigorous definition of what it means for a property to hold for almost all graphs. − − To generate an Erdős–Rényi model <math>G(n, p) − − </math> two parameters must be specified: the total number of nodes {{mvar|n}} and the probability {{mvar|p}} that a random pair of nodes has an edge. − − Because the model is generated without bias to particular nodes, the degree distribution is binomial: for a randomly chosen vertex <math>v</math>, − : <math>P(\deg(v) = k) = {n-1\choose k} p^k (1-p)^{n-1-k}.</math> − − In this model the clustering coefficient is {{math|0}} [[Almost surely|a.s]]. The behavior of <math>G(n, p) − − </math> can be broken into three regions. − − ''Subcritical'' <math>n p < 1 − − </math>: All components are simple and very small, the largest component has size <math>|C_1| = O(\log n) − − </math>; − − ''Critical'' <math>n p = 1 − − </math>: <math>|C_1| = O(n^\frac{2}{3}) − − </math>; − − ''Supercritical'' <math>n p >1 − − </math>:<math>|C_1| \approx yn − </math> where <math>y = y(n p) − − </math> is the positive solution to the equation <math>e^{-p n y }=1-y − − </math>. − − The largest connected component has high complexity. All other components are simple and small <math>|C_2| = O(\log n) − − </math>.
→Erdős–Rényi random graph model
网络模型是理解经验上复杂网络内相互作用的基础，各种各样的[[随机图]]生成模型生成的网络结构可与现实中的复杂网络进行比较。
网络模型是理解经验上复杂网络内相互作用的基础，各种各样的[[随机图]]生成模型生成的网络结构可与现实中的复杂网络进行比较。
=== Erdős–Rényi 随机图模型 ===
=== Erdős–Rényi 随机图模型 ===