Butterfly model slides Topological Model Butterfly Objective Develop

Butterfly model slides

Topological Model: “Butterfly” • Objective: Develop model to help explain behavioral mechanisms that cause observed properties, and to aid in forecasting. • Properties: – Constant/oscillating NLCC’s – Densification (nodes vs edges) – Shrinking diameter (after “gelling point”) – Heavy-tailed degree distribution – Weight properties – Emergent, local, intuitive behavior 2

Topological Model: “Butterfly” • Main idea: 3 parameters – phost: Chooses several hosts (“social butterfly”) – pstep: Explores local networks in random walk – plink: Links probabilistically 3

Topological Model: “Butterfly” • Main idea: 3 parameters – phost: Chooses several hosts (“social butterfly”) – pstep: Explores local networks in random walk – plink: Links probabilistically 4

Topological Model: “Butterfly” • Main idea: 3 parameters – phost: Chooses several hosts (“social butterfly”) – pstep: Explores local networks in random walk – plink: Links probabilistically 5

Topological Model: “Butterfly” • Main idea: 3 parameters – phost: Chooses several hosts (“social butterfly”) – pstep: Explores local networks in random walk – plink: Links probabilistically 6

Topological Model: “Butterfly” • Main idea: 3 parameters – phost: Chooses several hosts (“social butterfly”) – pstep: Explores local networks in random walk – plink: Links probabilistically 7

Topological Model: “Butterfly” • Theorem: Number of visits in each local neighborhood will follow power law. – Helps lead to heavy tailed outdegree-distribution. • Proof: See Ch. 4. 1. • Also proved that Butterfly reproduces the other properties related to components. 8

Topological Model: “Butterfly” Densification log(node s) Postnet (real) Shrinking diameter 1. slope=1. 1 Diameter log(edges) Time log(edge s) Model (synthetic) slope=1. 17 log(nodes) Diameter Time 9

Topological Model: “Butterfly” Oscillating NLCCs Power-law degree distribution Postnet (real) Model(synt hetic) Log(cou nt) NLCC size Nodes slope=-2 Log(degree) 10

Topological model: “Butterfly” Observed properties: üDensification üShrinking diameter üHeavy-tailed degree distribution üOscillating NLCCs Also (in weighted version, see thesis): üEigenvalue power law üWeight power laws üBursty weight additions 11