DCS/CSCI 2350: Social & Economic Networks Are all the links in - - PDF document
10/8/20 DCS/CSCI 2350: Social & Economic Networks Are all the links in a network the same? What is the effect of different types of links? The strength of weak ties edges Reading: Ch 3 of Easley-Kleinberg Mohammad T . Irfan 1
edges
u Agenda
u Connect local/interpersonal properties to
global/structural properties
u Mathematically prove this local to global link u Show that the “critical” ties are actually weak ties
u Acquaintances, not friends, hold critical
A B C B and C are very likely to become friends (Rapoport, 1953)
u Triadic closure increases clustering coeff.
u Reasons why triadic closure happens
1.
Opportunity for B and C to meet
2.
B and C can trust each other
3.
A wants to reduce stress by making B and C friends
u Teen suicide <--> low (local) clustering coefficient
(Bearman and Moody, 2004)
u An edge whose endpoints do
not have any common friend
ó An edge which is not a side of
any triangle
ó An edge whose deletion
causes the distance between its endpoints to be > 2
Next: under some condition, every local bridge must be a “weak” tie H I E G F B D C A
Local bridges have global implications.
u Tie-strength (simplifying gradation, temporal
u Weak (acquaintance) u Strong (friend)
u Strong Triadic Closure Property (STCP)
Definition.
Node-level property Edge-level property
u If a node A satisfies STCP and has at least 2
u Proof.
Colleagues High school friends