Abstract
The intense development of computing techniques and the increasing volumes of produced data raise many modelling and analysis challenges. There is a need to represent and analyse information that is: complex –due to the presence of massive and highly heterogeneous data–, dynamic –due to interactions, time, external and internal evolutions–, connected and distributed in networks. We argue in this work that relevant concepts to address these challenges are provided by three ingredients: labelled graphs to represent networks of data or objects; rewrite rules to deal with concurrent local transformations; strategies to express control versus autonomy and to focus on points of interests. To illustrate the use of these concepts, we choose to focus our interest on social networks analysis, and more precisely in this paper on random network generation. Labelled graph strategic rewriting provides a formalism in which different models can be generated and compared. Conversely, the study of social networks, with their size and complexity, stimulates the search for structure and efficiency in graph rewriting. It also motivated the design of new or more general kinds of graphs, rules and strategies (for instance, to define positions in graphs), which are illustrated here. This opens the way to further theoretical and practical questions for the rewriting community.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
For instance from http://snap.stanford.edu.
- 2.
Porgy website: http://tulip.labri.fr/TulipDrupal/?q=porgy.
References
Andrei, O., Fernández, M., Kirchner, H., Melançon, G., Namet, O., Pinaud, B.: PORGY: strategy-driven interactive transformation of graphs. In: Echahed, R. (ed.) 6th International Workshop on Computing with Terms and Graphs, vol. 48, pp. 54–68 (2011)
Andrei, O., Kirchner, H.: A rewriting calculus for multigraphs with ports. In: Proceedings of RULE 2007. Electronic Notes in Theoretical Computer Science, vol. 219, pp. 67–82 (2008)
Andrei, O., Kirchner, H.: A higher-order graph calculus for autonomic computing. In: Lipshteyn, M., Levit, V.E., McConnell, R.M. (eds.) Graph Theory, Computational Intelligence and Thought. LNCS, vol. 5420, pp. 15–26. Springer, Heidelberg (2009)
Balland, E., Brauner, P., Kopetz, R., Moreau, P.-E., Reilles, A.: Tom: piggybacking rewriting on Java. In: Baader, F. (ed.) RTA 2007. LNCS, vol. 4533, pp. 36–47. Springer, Heidelberg (2007)
Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)
Barendregt, H.P., van Eekelen, M.C.J.D., Glauert, J.R.W., Kennaway, J.R., Plasmeijer, M.J., Sleep, M.R.: Term graph rewriting. In: de Bakker, J.W., Nijman, A.J., Treleaven, P.C. (eds.) Proceedings of PARLE, Parallel Architectures and Languages Europe. LNCS, vol. 259-II, pp. 141–158. Springer, Heidelberg (1987)
Barthelmann, K.: How to construct a hyperedge replacement system for a context-free set of hypergraphs. Technical report, Universität Mainz, Institut für Informatik (1996)
Batagelj, V., Brandes, U.: Efficient generation of large random networks. Phys. Rev. E 71, 036113 (2005)
Bertuzzo, E., Casagrandi, R., Gatto, M., Rodriguez-Iturbe, I., Rinaldo, A.: On spatially explicit models of cholera epidemics. J. R. Soc. Interface 7(43), 321–333 (2010)
Borovanský, P., Kirchner, C., Kirchner, H., Moreau, P.-E., Ringeissen, C.: An overview of ELAN. ENTCS 15, 55–70 (1998)
Brandes, U., Wagner, D.: Analysis and visualization of social networks. In: Jünger, M., Mutzel, P. (eds.) Graph Drawing Software. Mathematics and Visualization, pp. 321–340. Springer, Heidelberg (2004)
Carrington, P.J., Scott, J., Wasserman, S.: Models and Methods in Social Network Analysis. Structural Analysis in the Social Sciences. Cambridge University Press, Cambridge (2005)
Cartwright, D., Harary, F.: Structural balance: a generalization of Heider’s theory. Psychol. Rev. 63, 277–293 (1956)
Chen, W., Collins, A., Cummings, R., Ke, T., Liu, Z., Rincón, D., Sun, X., Wang, Y., Wei, W., Yuan, Y.: Influence maximization in social networks when negative opinions may emerge and propagate. In: Proceedings of the 11th SIAM International Conference on Data Mining, SDM 2011, pp. 379–390 (2011)
Chen, W., Wang, C., Wang, Y.: Scalable influence maximization for prevalent viral marketing in large-scale social networks. In: Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2010, pp. 1029–1038. ACM (2010)
Corradini, A., Montanari, U., Rossi, F., Ehrig, H., Heckel, R., Löwe, M.: Algebraic approaches to graph transformation - part I: basic concepts and double pushout approach. In: Handbook of Graph Grammars and Computing by Graph Transformations. Foundations, vol. 1, pp. 163–246. World Scientific (1997)
Dodds, P.S., Watts, D.J.: A generalized model of social and biological contagion. J. Theor. Biol. 232(4), 587–604 (2005)
Erdős, P., Rényi, A.: On the evolution of random graphs. Publ. Math. Inst. Hungar. Acad. Sci. 5, 17–61 (1960)
Fernández, M., Kirchner, H., Pinaud, B.: Strategic port graph rewriting: an interactive modelling and analysis framework. Research report, Inria, January 2016
Fernández, M., Kirchner, H., Namet, O.: A strategy language for graph rewriting. In: Vidal, G. (ed.) LOPSTR 2011. LNCS, vol. 7225, pp. 173–188. Springer, Heidelberg (2012)
Fernández, M., Kirchner, H., Pinaud, B.: Strategic port graph rewriting: an interactive modelling and analysis framework. In: Bosnacki, D., Edelkamp, S., Lluch-Lafuente, A., Wijs, A. (eds.) Proceedings of the 3rd Workshop on GRAPH Inspection and Traversal Engineering, GRAPHITE 2014. EPTCS, vol. 159, pp. 15–29 (2014)
Goyal, A., Bonchi, F., Lakshmanan, L.V.S.: Learning influence probabilities in social networks. In: Proceedings of the 3rd ACM International Conference on Web Search and Data Mining, WSDM 2010, pp. 241–250. ACM (2010)
Granovetter, M.: Threshold models of collective behavior. Am. J. Sociol. 83(6), 1420 (1978)
Habel, A., Müller, J., Plump, D.: Double-pushout graph transformation revisited. Math. Struct. Comput. Sci. 11(5), 637–688 (2001)
Kejžar, N., Nikoloski, Z., Batagelj, V.: Probabilistic inductive classes of graphs. J. Math. Sociol. 32(2), 85–109 (2008)
Kempe, D., Kleinberg, J.M., Tardos, É.: Influential nodes in a diffusion model for social networks. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 1127–1138. Springer, Heidelberg (2005)
Kivelä, M., Arenas, A., Barthelemy, M., Gleeson, J.P., Moreno, Y., Porter, M.A.: Multilayer networks. J. Complex Netw. 2(3), 203–271 (2014). doi:10.1093/comnet/cnu016. http://comnet.oxfordjournals.org/content/2/3/203.abstract
Lafont, Y.: Interaction nets. In: Proceedings of the 17th ACM Symposium on Principles of Programming Languages (POPL 1990), pp. 95–108. ACM Press (1990)
Leskovec, J., Huttenlocher, D., Kleinberg, J.: Signed networks in social media. In: Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, CHI 2010, pp. 1361–1370. ACM (2010)
Milgram, S.: The small world problem. Psychol. Today 2, 60–67 (1967)
Newman, M., Barabási, A.-L., Watts, D.J.: The Structure and Dynamics of Networks. Princeton Studies in Complexity. Princeton University Press, New Jersey (2006)
Nick, B., Lee, C., Cunningham, P., Brandes, U.: Simmelian backbones: amplifying hidden homophily in facebook networks. In: 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM), pp. 525–532, August 2013
Pinaud, B., Melançon, G., Dubois, J.: PORGY: a visual graph rewriting environment for complex systems. Comput. Graph. Forum 31(3), 1265–1274 (2012)
Plump, D.: Term graph rewriting. In: Ehrig, H., Engels, G., Kreowski, H.-J., Rozenberg, G. (eds.) Handbook of Graph Grammars, Computing by Graph Transformations. Applications, Languages, and Tools, vol. 2, pp. 3–61. World Scientific, Singapore (1998)
Plump, D.: The graph programming language GP. In: Bozapalidis, S., Rahonis, G. (eds.) CAI 2009. LNCS, vol. 5725, pp. 99–122. Springer, Heidelberg (2009)
Scott, J., Carrington, P.J.: The SAGE Handbook of Social Network Analysis. SAGE, New York (2011)
Vallet, J., Kirchner, H., Pinaud, B., Melançon, G.: A visual analytics approach to compare propagation models in social networks. In: Rensink, A., Zambon, E. (eds.) Proceedings of the Graphs as Models, GaM 2015. EPTCS, vol. 181, pp. 65–79 (2015)
Visser, E.: Stratego: a language for program transformation based on rewriting strategies system description of Stratego 0.5. In: Middeldorp, A. (ed.) RTA 2001. LNCS, vol. 2051, pp. 357–361. Springer, Heidelberg (2001)
Wang, L., Du, F., Dai, H.P., Sun, Y.X.: Random pseudofractal scale-free networks with small-world effect. Eur. Phys. J. B - Condens. Matter Complex Syst. 53(3), 361–366 (2006)
Watts, D.J.: A simple model of global cascades on random networks. Proc. Nat. Acad. Sci. 99(9), 5766–5771 (2002)
Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998)
Wonyeol, L., Jinha, K., Hwanjo, Y.: CT-IC: Continuously activated and time-restricted independent cascade model for viral marketing. In: 2012 IEEE 12th International Conference on Data Mining (ICDM), pp. 960–965 (2012)
Acknowledgements
We thank Guy Melançon (University of Bordeaux) and all the other members of the Porgy project. We also thank the anonymous reviewer for carefully reading this paper and making valuable suggestions for improvement.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Fernández, M., Kirchner, H., Pinaud, B., Vallet, J. (2016). Labelled Graph Rewriting Meets Social Networks. In: Lucanu, D. (eds) Rewriting Logic and Its Applications. WRLA 2016. Lecture Notes in Computer Science(), vol 9942. Springer, Cham. https://doi.org/10.1007/978-3-319-44802-2_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-44802-2_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-44801-5
Online ISBN: 978-3-319-44802-2
eBook Packages: Computer ScienceComputer Science (R0)