Abstract Networks. WWW (2000) Scientific Collaboration Girvan & Newman (2002)

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Presentation transcript:

Abstract Networks

WWW (2000)

Scientific Collaboration Girvan & Newman (2002)

Sexual Contact Potterat et al. (2002)

Community Structure Moody (2001)

SocialFriendships Business Relationships Sexual relationships Small World Networks InformationWWW citation Thesaurus TechnologicalInternet Power Grid Train, Plane, Road, River Routes BiologicalNeural Network Metabolic Protein Interactions Circulatory System

Some Questions to ask About Networks Technological Networks (eg Internet) Information Networks (eg WWW) Social Networks

Random N = 20 Av-k = 5

Bell-Shaped Distribution

Barabasi’s Results

Twitter

Power-Law Distribution

P(k) prob that node is connected to k other nodes Web Log-log

Scale Free Dia = 4

How are Scale-Free Networks Built?

Applications of Abstract Scale-Free Thinking

Diameter of the Web Albert, Jeong & Barabasi (1999) Nature. Definition 1 (Barabasi) “average of the shortest paths between all nodes. Definition 2 The longest of all shortest nodes.

Scale Free Dia = 4

Scale Free Dia = 4

Random Attack Nodes 1,12,18

Targeted Attack Nodes 4,5,6

Random N = 20 Av-k = 5

Random Attack Nodes 1,2,18

Targeted Attack Nodes 1,2,18

Network Resilience

Small Worlds – Social Networks N people in the world with z acquaintances. How many links l needed to get from and person to any other person?

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