# An Evolutionary and Graph-Rewriting based Approach to Graph Generation

### Aaron Barry, Josephine Griffith, Colm O'Riordan

#### Abstract

This paper describes an evolutionary computation based graph rewriting approach to generating classes of graphs that exhibit a set of desired global features. A set of rules are used to generate, in a constructive manner, classes of graphs. Each rule represents a transformation from one graph to another. Each of these transformations causes local changes in the graph. Probabilities can be assigned to the rules which govern the frequency with which they will be applied. By assigning these probabilities correctly, one can generate graphs exhibiting desirable global features. However, choosing the correct probability distribution to generate the desired graphs is not an easy task for certain graphs and the task of finding the correct settings for these graphs may represent a difficult search space for the evolutionary algorithms. In order to generate graphs exhibiting desirable features, an evolutionary algorithm is used to find the suitable probabilities to assign to the rules. The fitness function rewards graphs that exhibit the desired properties. We show, using a small rule base, how a range of graphs can be generated.

#### References

- Ílvarez-García, S., Baeza-Yates, R., Brisaboa, N. R., Larriba-Pey, J.-L., and Pedreira, O. (2014). Automatic multi-partite graph generation from arbitrary data. Journal of Systems and Software, 94:72-86.
- Bach, B., Spritzer, A., Lutton, E., and Fekete, J.-D. (2013). Interactive random graph generation with evolutionary algorithms. In Graph Drawing, pages 541-552. Springer.
- Barabási, A.-L. and Albert, R. (1999). Emergence of scaling in random networks. science, 286(5439):509-512.
- Chung, F. and Lu, L. (2002). The average distances in random graphs with given expected degrees. Proceedings of the National Academy of Sciences, 99(25):15879- 15882.
- Erdo?s, P. and Rényi, A. (1961). On the evolution of random graphs. Bull. Inst. Internat. Statist, 38(4):343-347.
- Gang, W., Kun, G., Han-Xin, Y., and Bing-Hong, W. (2008). Role of clustering coefficient on cooperation dynamics in homogeneous networks. Chinese Physics Letters, 25(6):2307.
- Gilbert, E. N. (1959). Random graphs. The Annals of Mathematical Statistics, pages 1141-1144.
- Heath, L. S. and Parikh, N. (2011). Generating random graphs with tunable clustering coefficients. Physica A: Statistical Mechanics and its Applications, 390(23):4577-4587.
- Herrera, C. and Zufiria, P. J. (2011). Generating scalefree networks with adjustable clustering coefficient via random walks. arXiv preprint arXiv:1105.3347.
- Holme, P. and Kim, B. J. (2002). Growing scale-free networks with tunable clustering. Physical review E, 65(2):026107.
- Kernighan, B. W. and Lin, S. (1970). An efficient heuristic procedure for partitioning graphs. Bell System Technical Journal, 49(2):291-307.
- Leskovec, J., Chakrabarti, D., Kleinberg, J., and Faloutsos, C. (2005a). Realistic, mathematically tractable graph generation and evolution, using kronecker multiplication. In Knowledge Discovery in Databases: PKDD 2005, pages 133-145. Springer.
- Leskovec, J., Chakrabarti, D., Kleinberg, J., Faloutsos, C., and Ghahramani, Z. (2010). Kronecker graphs: An approach to modeling networks. The Journal of Machine Learning Research, 11:985-1042.
- Leskovec, J., Kleinberg, J., and Faloutsos, C. (2005b). Graphs over time: densification laws, shrinking diameters and possible explanations. In Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining, pages 177-187. ACM.
- Li, M. and O'Riordan, C. (2013). The effect of clustering coefficient and node degree on the robustness of cooperation. In Evolutionary Computation (CEC), 2013 IEEE Congress on, pages 2833-2839. IEEE.
- Newman, M. E. (2000). Models of the small world. Journal of Statistical Physics, 101(3-4):819-841.
- O'Riordan, C., Cunningham, A., and Sorensen, H. (2008). Emergence of cooperation in n-player games on small world networks. In ALIFE, pages 436-442.
- Penrose, M. (2003). Random geometric graphs, volume 5. Oxford University Press Oxford.
- Pohl, I. (1970). Heuristic search viewed as path finding in a graph. Artificial Intelligence , 1(3):193-204.
- Seshadhri, C., Kolda, T. G., and Pinar, A. (2012). Community structure and scale-free collections of erdo?s-rényi graphs. Physical Review E, 85(5):056109.
- Shuai, H.-H., Yang, D.-N., Yu, P. S., Shen, C.-Y., and Chen, M.-S. (2013). On pattern preserving graph generation. In Data Mining (ICDM), 2013 IEEE 13th International Conference on, pages 677-686. IEEE.
- Stanley, K. O., Bryant, B. D., and Miikkulainen, R. (2003). Evolving adaptive neural networks with and without adaptive synapses. In Evolutionary Computation, 2003. CEC'03. The 2003 Congress on, volume 4, pages 2557-2564. IEEE.
- Stanley, K. O. and Miikkulainen, R. (2002). Evolving neural networks through augmenting topologies. Evolutionary Computation, 10(2):99-127.
- Wood, D. (1969). A technique for colouring a graph applicable to large scale timetabling problems. The Computer Journal, 12(4):317-319.

#### Paper Citation

#### in Harvard Style

Barry A., Griffith J. and O'Riordan C. (2015). **An Evolutionary and Graph-Rewriting based Approach to Graph Generation** . In *Proceedings of the 7th International Joint Conference on Computational Intelligence - Volume 1: ECTA,* ISBN 978-989-758-157-1, pages 237-243. DOI: 10.5220/0005597102370243

#### in Bibtex Style

@conference{ecta15,

author={Aaron Barry and Josephine Griffith and Colm O'Riordan},

title={An Evolutionary and Graph-Rewriting based Approach to Graph Generation},

booktitle={Proceedings of the 7th International Joint Conference on Computational Intelligence - Volume 1: ECTA,},

year={2015},

pages={237-243},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005597102370243},

isbn={978-989-758-157-1},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 7th International Joint Conference on Computational Intelligence - Volume 1: ECTA,

TI - An Evolutionary and Graph-Rewriting based Approach to Graph Generation

SN - 978-989-758-157-1

AU - Barry A.

AU - Griffith J.

AU - O'Riordan C.

PY - 2015

SP - 237

EP - 243

DO - 10.5220/0005597102370243