Why the nw model?年 Recall: the ws model's drawbacks 1)Isolation possibility (why?) 2)Difficult for mathematical analysis Advantage of the nw model 1)No isolation clusters (why?) 2) Easy for mathematical analysis 3) Equivalent to the ws model with O<p<<l
Why the NW model? • Recall: the WS model’s drawbacks: 1) Isolation possibility (why?) 2) Difficult for mathematical analysis • Advantage of the NW model 1) No isolation clusters (why?) 2) Easy for mathematical analysis 3) Equivalent to the WS model with 0<p<<1
Recall: Watts-Strogatz Model Regul Small-world Random p=1 Increasing randomness 0.8 C(p)/C(p) D L(p)/L(O) ⊥⊥⊥⊥L 0.0001 0.001 C(p): clustering coeff. L(p): average path length (Watts and Strogatz, Nature 393, 440(1998))
Recall: Watts-Strogatz Model C(p) : clustering coeff. L(p) : average path length (Watts and Strogatz, Nature 393, 440 (1998))
C nw.L nw. degree dist Example: Degree distribution N-1[ Kp R-K kp N-1-R+K P(k)= k-K/N-1 N How about the C nw? rewiring of links additron of tinks
C_nw, L_nw, Degree Dist. Example: Degree distribution How about the C_nw?
Recall: Criticisms and doubts ·J. Kleinfeld: Six Degrees of separation an urban myth? T Berman Six Degrees of separation fact or Friction M. Blastland other? How well are you connected ach Could we really all be connected to ea How to solve the doubts?
Recall: Criticisms and Doubts • J. Kleinfeld: Six Degrees of Separation: an urban myth? • T. Berman: Six Degrees of Separation: Fact or Friction? • M. Blastland: Could we really all be connected to each other? How well are you connected? …… How to solve the doubts?
A 500th person to the riaht of A Your Friends Friends Friends Only have local information to reach ur Friends Friend the(global)target Your Friends Given the network is You reachable in a definite (not many) steps The shortest path
Only have local information to reach the (global) target! Given the network is reachable in a definite (not many) steps. The shortest path