复旦大学：《网络科学导论 Introduction to Network Science》学生课堂辩论陈述_反方-Love is all you need

Love is all you need. A FEW WORDS ABOUT CALE-FREE NETWORKS 季宏字17307130251 何嘉诚17307130264 郁钧瑾17307130278

Love is all you need. A FEW WORDS ABOUT SCALE -FREE NETWORKS 季宏宇 17307130251 何嘉诚 17307130264 郁钧瑾 17307130278

Power Law p(k)kr How long is long tail?

Y O U R B R A N D Power Law 𝑝 𝑘 ~𝑘 _ 𝛾 How long is long tail?

Simon vs mandelbrot Al PK Fractal ON A CLASS OF SKEW DISTRIBUTION FUNCTIONS a paper a note further notes final note reply to final note post script to final note 大网络小世界 reply to post script oz<xm0

Simon VS Mandelbrot AI PK Fractal Y O U R B R A N D ON A CLASS OF SKEW DISTRIBUTION FUNCTIONS

varying definitions of " scale free just more heavy-tailed than exponential, Pr(k)xe-Ak not Pr(ki) o k-a exactly, but more plausible than alternatives lausibly Pr(k)ok a for any a · plausibly Pr(k)∝k- but for2<a<3only · plausibly Pr(k)∝ k but only in upper tail plausibly Pr(k)∝k-a except for exponential cutoff scale free is well defined mainly for simple graphs

Power law 1. Timeline 2 Scale- Free Network 3 Generation mechanism 4 Variants 5.Real Complicated Network

Power Law 1.Timeline 2.Scale-Free Network 3.Generation mechanism 4.Variants 5.Real Complicated Network

Timelin Elephant. the 19th cent Cow 95 100 Pareto &Man dmon Dog, Goat Personal Incor cHicken.. Cat kew istribution Dove. unction Mous 0.1 001 0.1 10 100 100010.000 Lons Body mass (kg) reat things kerber法则(双对坐标)

1955 Simon 1932 Kleiber the 19th century Pareto 1932 Zipf Only passions, great passions, can elevate the soul to great things Personal Income The Frequency of the Word Skew Distribution Function Timeline Mammalian basal metabolic rate

Scale-free Network

Scale-Free Network

Recent interest in scale-free networks started in 1999 with work by Albert-Laszlo Barabasi Barabasi and collaborators History coined the term"scale-free networkto describe the class of networks that exhibit a power-law degree distribution p(k)kY,y=3 1965 1976 Price Price the number of links to papers had a heavy cumulative advantage tailed distribution following a Pareto distribution or power law

History Recent interest in scale-free networks started in 1999 with work by Albert-László Barabási . Barabási and collaborators coined the term "scale-free network" to describe the class of networks that exhibit a power-law degree distribution. 𝑝 𝑘 ~𝑘 _ 𝛾 ,γ=3 1965 1976 Price Price the number of links to papers had a heavy- cumulative advantage tailed distribution following a Pareto distribution or power law

Generation mechanism Preferential HOT theory attachment generation Random orocess z<m20

generation Y O U R B R A N D Preferential attachment Self-organized criticality HOT theory Random process Generation mechanism

Broken power law Power Law with Curved power law exponential cutoff ∫(x)∝ I for ath f(x)xx°e f(x)∝x+x Another common distribution: power-aw with an exponential cutoff Variants lass ISolar mass]

Variants Broken Power Law Power Law with Curved Power Law exponential cutoff