Using Evolutionary Computing for Feature-driven Graph generation
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1. The document discusses using evolutionary computing techniques to generate graphs with specific structural properties. 2. It presents an approach that uses genetic algorithms and neural networks to evolve graph generating functions that can produce graphs with user-specified properties like number of nodes, edges, clustering coefficient, etc. 3. The results show this approach can generate graphs faster than other evolutionary algorithms for graph generation, though it has trouble scaling to graphs with over 1,000 nodes.
Using Evolutionary Computing for Feature-driven Graph generation
- 1. Using Evolutionary Computing for Feature- driven Graph Generation Merijn Verstraaten, Ana Lucia Varbanescu & Cees de Laat
- 3. 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
- 4. Structural Properties Number 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
- 5. Generator Wishlist Set of relevant properties Independently variable (if possible) Easy to extend set
- 6. 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
- 7. Representations Connectivity matrices Edge lists Generating functions Generators
- 8. 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
- 9. Pros & Cons Pros: Easy to implement primitives Fixed number of vertices Cons: Number of edges not fixed
- 10. Exponential Degree � � � � � � � � � � �� �� � �� �� �� ���������������� ������ ������ ����������� ������ ������������ ����������� ������������ �� � ����
- 11. Gaussian Degree � � � � � � � � � �� �� �� �� �� �� �� �� �� ��� ��� ��� ���������������� ������ ������ ������ ������ ������������ ������ ������������ �� � ��� � � ���
- 12. Uniform Degree � � � � � � �� �� �� �� �� �� �� �� �� ��� ��� ���������������� ������ ������ ������� ������ ������������ ������� ������������ �� � ����
- 13. Results + Substantially faster than Bach, et al. & Bailey, et al. - Graphs >1.000 vertices converge too slowly
- 14. Future Work Experiment with different primitives Evaluate the HyperNEAT approach Miscellaneous Observations Primitives matter (edgewise vs vertexwise) Need better mutation Minimum necessary size?
- 15. Questions? Suggestions? Comments? ... are welcome live or online! m.e.verstraaten@uva.nl a.l.varbanescu@uva.nl
- 16. 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
- 17. NeuroEvolution of Augmenting Topologies (NEAT) Pros: Very expressive Good results Cons: Scalability Slow… HyperNEAT: Generate generating functions Pros: ``Webscale’’ Cons: Unclear impact on expressivity
- 18. 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.