复旦大学：《网络科学导论 Introduction to Network Science》教学课件_6- Scale free networks

Network science An English introductory course for undergraduate students Lecturer: Dr. Cong LI ee@ Fudan University Adaptive Networks and Control Lab

Network Science Lecturer: Dr. Cong LI EE @ Fudan University —— An English introductory course for undergraduate students Adaptive Networks and Control Lab

Research History of Complex Networks Time(year) Characters Events 1736 Euler Seven Bridge Problem 1959 Erdos-Renyi Random Graph Theory 1967 Mis gra Small-world Experiments 1998 Watts-Strogatz Small-world Model 1999 Barabasi-Albert Scale-free networks/

Research History of Complex Networks Time (year) Characters Events 1736 Euler Seven Bridge Problem 1959 Erdös – Rényi Random Graph Theory 1967 Migram Small-world Experiments 1998 Watts-Strogatz Small-world Model 1999 Barabasi-Albert Scale-free networks

Some basic concepts in a network Clustering and Clustering coefficient C Distance and Average Path Length L Degree and Degree Distribution P(h

Some basic concepts in a network • Clustering and Clustering coefficient C • Distance and Average Path Length L • Degree and Degree Distribution P(k)

Recall: the er random graph model Erdos-Renyi Publ. Math. Inst. Hung. Acd. Sci. 5, 17 (1960) 0.10 E(XK)N R N nodes. each pair of nodes 0.05 are connected with =0.2 probability p 0.00L4 10 Degree Distribution P(k)

Recall: the ER random graph model Degree Distribution P(k)

Recall: the small-world model a) WS model re wiring of links b)NW model b addition of links Clustering coefficient C Average path length

Recall: the small-world model a) WS model b) NW model Clustering coefficient C Average Path Length L

ArPaNEt1974 LINCOLN Honolulu MOFF LBL CCA UTAH LLL BBNBBN Kjeller HAWAI AMES GWC CARNEGI AMES NCC XEROX PURDUE HARVARD TYMS RUTGERS FNWS BELVO ABERDEEN NORSAR DOCB URPAT MITRE CLA UCL AFWL ETAC RAN USC ■"TP"- Kan tilknyttes vertsmaskiner og terminale ●"MP" Kan tilknyttes Y RML vertsmaskine

ARPANET, 1974

From arpanet to INtErnet http:/en.wikipediaorg/wiki/historyoftheinternet

From ARPANET to INTERNET • http://en.wikipedia.org/wiki/History_of_the_Internet

In a very long period, the Internet is thought as a random network. as a product of God playing-dice E(XKWN 0.05 vertsmaskiner og terminale O 'IMP 0.00

• In a very long period, the Internet is thought as a random network, as a product of God￾playing-dice

God Does Not Play Dice 0奇 Einstein. 1926

God Does Not Play Dice • Einstein, 1926

The same is the truth for the internet WwW, and many large-scale networks A L. Barabasi and his group, 1999

• The same is the truth for the Internet, WWW, and many large-scale networks. A.L. Barabasi and his group, 1999