《社会网络研究导论》课程教学课件（讲稿）07 复杂网络讨论（小世界网络）

社会网络研究导论（7）复杂网络讨论（1）Complex network何晓晨

社会网络研究导论（ 7 ） 复杂网络讨论(1) Complex network 何晓晨

复杂网络？我们已经学习了经典社会网络分析的内容，复杂网络是什么？We've learned about classic social network analysis, what is a complexnetwork?什么是复杂？What is complexity?- Consisting of interconnected or interwoven parts; compositeComposedoftwoormoreunits

复杂网络？ • 我们已经学习了经典社会网络分析的内容，复杂网络是什么？ • We've learned about classic social network analysis, what is a complex network? • 什么是复杂？ • What is complexity? – Consisting of interconnected or interwoven parts; composite. – Composed of two or more units –

复杂网络Complexnetworklinear and non-linear线性与非线性The nature of linearity?一线性的本质？The superposition or additivity of·线性现象的可选加性或可加性linear phenomena·线性现象的可数乘性Countabilityof linearphenomena·线性演化方程在有限时间内一般不会出现奇异性,也即线性有它特有的·Linear evolution equation does notappear singularity in limited time,that简单性is, linear has its unique simplicity有限时可叠线性可数乘性间非奇加性世界异简单(har)=0(+x)=0F(αx)=0性衍生性n个解（维数）构成线性空间Why is the linear world so brilliant?为什么线性世界会如此辉煌？

复杂网络Complex network • 线性与非线性 – 线性的本质？ • 线性现象的可迭加性或可加性 • 线性现象的可数乘性 • 线性演化方程在有限时间内一般不 会出现奇异性,也即线性有它特有的 简单性 – 为什么线性世界会如此辉煌？ • linear and non-linear • The nature of linearity？ • The superposition or additivity of linear phenomena • Countability of linear phenomena • Linear evolution equation does not appear singularity in limited time, that is, linear has its unique simplicity • Why is the linear world so brilliant？

复杂网络Complexnetwork线性与非线性linearandnon-linear一非线性non-linear一(1)Contradictoryfactors-(2)Interactioncnuus复杂性非线性变化非线不可方程出现奇叠加性世非周期，→异性，突变界性内在危机性一初值整体不(1)矛盾因素?敏感等于各(2)相互作用不可个局部4重复之和

复杂网络Complex network • 线性与非线性 linear and non-linear – 非线性 non-linear – (1) Contradictory factors – (2) Interaction (1)矛盾因素 (2)相互作用

复杂网络Complexnetwork·网络结构构造Network structure-规则 Regular

复杂网络Complex network • 网络结构构造 Network structure – 规则 Regular

复杂网络Complexnetwork·网络结构构造Network structure一规则Regular一随机Random

复杂网络Complex network • 网络结构构造 Network structure – 规则 Regular – 随机 Random

复杂网络Complexnetwork·网络结构构造Network structure一规则Regular-随机RandomΛN-1-kP(k, = k) =pC

复杂网络Complex network • 网络结构构造 Network structure – 规则 Regular – 随机 Random k N k i p p k N P k k − − −         − = = 1 (1 ) 1 ( )

复杂网络Complexnetwork·网络结构构造Network structure一规则Regular-随机Random-其它？OthersN.N-1-kP(k, = k) =DT·实际网络Real network

复杂网络Complex network • 网络结构构造 Network structure – 规则 Regular – 随机 Random – 其它？Others • 实际网络 Real network k N k i p p k N P k k − − −         − = = 1 (1 ) 1 ( )

复杂网络·网络结构复杂性Network structure complexity一小世界现象(Small-wordPhenomena)-无标度特征(Scale-freeProperties)一社群结构(Community Structure)·网络动力学Network dynamics

复杂网络 • 网络结构复杂性 Network structure complexity – 小世界现象（Small-word Phenomena） – 无标度特征（Scale-free Properties） – 社群结构（Community Structure） • 网络动力学 Network dynamics

小世界网络的发展What is‘small-world'?‘SmallWorld Experiment”social psychologistStanleyMilgram'ssmallworldexperimentconfirmedthattwostrangers could beconnected in sixdegrees.1967

‘Small World Experiment’ social psychologist Stanley Milgram’s small world experiment confirmed that two strangers could be connected in six degrees. 1967 . What is ‘small￾world’? 小世界网络的发展