using evolutionary computing for feature-driven graph generation

Using Evolutionary Computing for Feature-

driven Graph GenerationMerijn Verstraaten, Ana Lucia Varbanescu &

Cees de Laat

Performance Quiz

Structural Properties#V #E ACC Triangles Diameter

90% Diameter

as-Skitter 1.696.415 11.095.298 0,2581 28.769.868 25 6

cit-Patents 3.774.768 16.518.948 0,0757 7.515.023 22 9,4

email-EuAll 265.214 420.045 0,0671 267.313 14 4,5

Facebook 4.039 88.234 0,6055 1.612.010 8 4,7

GPlus 107.614 13.673.453 0,4901 1.073.677.742 6 3

roadNet-CA 1.965.206 2.766.607 0,0464 120.676 849 500

roadNet-TX 1.379.917 1.921.660 0,047 82.869 1.054 670

soc-Livejournal 4.847.571 68.993.773 0,2742 285.730.264 16 6,5

Twitter 81.306 1.768.149 0,5653 13.082.506 7 4,5

web-BerkStan 685.230 7.600.595 0,5967 64.690.980 514 9,9

web-Google 875.713 5.105.039 0,5143 13.391.903 21 8,1

wikiTalk 2.394.385 5.021.410 0,0526 9.203.519 9 4

Structural PropertiesNumber of vertices

Number of edges

Edge properties

Vertex properties

Directivity

Connectivity

Centrality – betweenness, degree, edge, PageRank(?)

Chromatic number

Cycles

Assortativity

Treewidth

Average degree

Average distance

Diameter

Max degree

Degree distribution

Clustering Coefficient

Number of triangles

Max-clique

Modularity

Eigenvalue and second eigenvalue

Degeneracy

Motif profile

Generator Wishlist

Set of relevant properties

Independently variable (if possible)

Easy to extend set

Start

Generate intial population

Determine fitness

Acceptable solution found

Select parents Crossover

Mutation

Select survivors

End Yes

No

Evolutionary Computing

Good at:

Large search space

Complex, interdependent parameters

Representations

Connectivity matrices

Edge lists

Generating functions

Generators

0

1

2

3

4

5

G

A

B

E

D

C

F

Connectivity Matrix

0 1 2 3 4 5

0 0 1 0 0 1 0

1 0 0 1 0 1 0

2 0 0 0 1 0 0

3 0 0 0 0 1 0

4 0 0 0 0 0 0

5 0 0 0 1 0 0

Pros & Cons

Pros:

Easy to implement primitives

Fixed number of vertices

Cons:

Number of edges not fixed

Exponential Degree

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Gaussian Degree

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Uniform Degree

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Results

+ Substantially faster than Bach, et al. & Bailey, et al.

- Graphs >1.000 vertices converge too slowly

Future WorkExperiment with different primitives

Evaluate the HyperNEAT approach

Miscellaneous ObservationsPrimitives matter (edgewise vs vertexwise)

Need better mutation

Minimum necessary size?

Questions? Suggestions? Comments?

... are welcome live or online!

m.e.verstraaten@uva.nl

a.l.varbanescu@uva.nl

Existing Generators

Complex Networks: Erdös-Rényi R-MAT Kronecker graphs

Misc: Social networks Freescale Power law etc.

Problems: Focus on social graphs Limited expressivity Not easily extensible

NeuroEvolution of Augmenting Topologies

(NEAT)Pros:

Very expressive Good results

Cons: Scalability Slow…

HyperNEAT: Generate generating functions

Pros: ``Webscale’’

Cons: Unclear impact on expressivity

More…Bach, et al.

Interactive random graph generation with evolutionary algorithms

Bailey, et al.

Automatic generation of graph models for complex networks by genetic programming.