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 <k> 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