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
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Topological Model: “Butterfly”
• Main idea: 3 parameters
– phost: Chooses several hosts (“social butterfly”)
– pstep: Explores local networks in random walk
– plink: Links probabilistically
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Topological Model: “Butterfly”
• Main idea: 3 parameters
– phost: Chooses several hosts (“social butterfly”)
– pstep: Explores local networks in random walk
– plink: Links probabilistically
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Topological Model: “Butterfly”
• Main idea: 3 parameters
– phost: Chooses several hosts (“social butterfly”)
– pstep: Explores local networks in random walk
– plink: Links probabilistically
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Topological Model: “Butterfly”
• Main idea: 3 parameters
– phost: Chooses several hosts (“social butterfly”)
– pstep: Explores local networks in random walk
– plink: Links probabilistically
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Topological Model: “Butterfly”
• Main idea: 3 parameters
– phost: Chooses several hosts (“social butterfly”)
– pstep: Explores local networks in random walk
– plink: Links probabilistically
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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.
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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
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Topological Model: “Butterfly”
Oscillating NLCCs
Power-law degree distribution
Postnet
(real)
Model(synt
hetic)
Log(cou
nt)
NLCC
size
Nodes
slope=-2
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Log(degree)
Topological model: “Butterfly”
Observed properties:
Densification
Shrinking diameter
Heavy-tailed degree distribution
Oscillating NLCCs
Also (in weighted version, see thesis):
Eigenvalue power law
Weight power laws
Bursty weight additions
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