Exploring the Community Structure of Complex Networks

Drago, Carlo (2015): Exploring the Community Structure of Complex Networks. Published in: Annali MEMOTEF No. 2016 (2016)

Abstract

Regarding complex networks, one of the most relevant problems is to understand and to explore community structure. In particular it is important to define the network organization and the functions associated to the different network partitions. In this context, the idea is to consider some new approaches based on interval data in order to represent the different relevant network components as communities. The method is also useful to represent the network community structure, especially the network hierarchical structure. The application of the methodologies is based on the Italian interlocking directorship network.

• Item Type: MPRA Paper
• Language: English
• Keywords: Complex Networks, Community Detection, Communities, Interval Data, Interlocking Directorates
• Subjects: C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C60 - General; L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance > L14 - Transactional Relationships ; Contracts and Reputation ; Networks

References

Albert, R., & Barabasi, A. L. (2002). Statistical mechanics of complex networks. Reviews of modern physics, 74(1), 47.

Barabasi, A.-L. and Albert R. (1999). Emergence of scaling in random networks Science, 286 509--512.

Barabasi, A. L., Dezso, Z., Ravasz, E., Yook, S. H., & Oltvai, Z. (2003). Scale--Free and Hierarchical Structures in Complex Networks. In Modelling of Complex Systems: Seventh Granada Lectures (Vol. 661, No. 1, pp. 1-16). AIP Publishing.

Bellenzier, L., & Grassi, R. (2014). Interlocking directorates in Italy: persistent links in network dynamics. Journal of Economic Interaction and Coordination,9(2), 183-202.

Billard, L. (2008). Some analyses of interval data. CIT. Journal of Computing and Information Technology, 16(4), 225-233.

Billard, L., & Diday, E. (2003) From the statistics of data to the statistics of knowledge: symbolic data analysis. Journal of the American Statistical Association, 98(462), 470-487.

Bock, H. H., & Diday, E. (Eds.). (2000). Analysis of symbolic data: exploratory methods for extracting statistical information from complex data. Springer Science & Business Media.

Brandes, U. (2001). A faster algorithm for betweenness centrality. Journal of mathematical sociology, 25(2), 163-177.

Brito, P., & Duarte Silva, A. P. (2012). Modelling interval data with Normal and Skew-Normal distributions. Journal of Applied Statistics, 39(1), 3-20.

Clauset, A., Newman, M. E., & Moore, C. (2004). Finding community structure in very large networks. Physical review E, 70(6), 066111.

Csardi G, Nepusz T: The igraph software package for complex network research, InterJournal, Complex Systems 1695. 2006. http://igraph.org

Costa, L. D. F., Rodrigues, F. A., Travieso, G., & Villas Boas, P. R. (2007). Characterization of complex networks: A survey of measurements. Advances in Physics, 56(1), 167-242.

Dequiedt, V., & Zenou, Y. (2014). Local and Consistent Centrality Measures in Networks. Working Paper

Diday, E., &Noirhomme-Fraiture, M. (Eds.). (2008). Symbolic data analysis and the SODAS software (pp. 1-457). J. Wiley & Sons.

Drago C., Balzanella A. (2015) "Non-metric MDS Consensus Community Detection” Advances in Statistical Models for Data Analysis, Edited by Morlini Isabella, Minerva Tommaso, Vichi Maurizio, 08/2015; Springer

Drago, C. and Millo, F. and Ricciuti, R. and Santella, P. (2014) ” Corporate Governance Reforms, Interlocking Directorship and Company Performance in Italy”. International Review of Law and Economics, Volume 41, March 2015, Pages 38–49.

Drago, C. and Ricciuti, R. and Santella, P. (2015) “An Attempt to Disperse the Italian Interlocking Directorship Network: Analyzing the Effects of the 2011 Reform”. Working Paper. Available at SSRN:http://ssrn.com/abstract=2580700

Erdos, P. and Renyi, A., On random graphs, PublicationesMathematicae 6, 290--297 (1959).

Fortunato, S. (2010) Community detection in graphs. Physics Reports, 486(3), 75-174.

Gioia, F., &Lauro, C. N. (2005) Basic statistical methods for interval data. Statisticaapplicata, 17(1).

Giordano, G., & Brito, M. P. (2012) Network Data as Complex Data Objects: An Approach Using Symbolic Data Analysis. Analysis and Modelling of Complex Data in Behavioural and Social Sciences, 38.

Lancichinetti, A., & Fortunato, S. (2009). Community detection algorithms: a comparative analysis. Physical review E, 80(5), 056117.

Lancichinetti, A., & Fortunato, S. (2012). Consensus clustering in complex networks. Scientific reports, 2.

Lauro, C. N., & Palumbo, F. (2000). Principal component analysis of interval data: a symbolic data analysis approach. Computational statistics, 15(1), 73-87.

Leskovec J., Kleinberg J. and Faloutsos C. (2005) “Graphs over time: densification laws, shrinking diameters and possible explanations” KDD '05: Proceeding of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining, 177--187, 2005.

Leskovec, J., Lang, K. J., & Mahoney, M. (2010, April). Empirical comparison of algorithms for network community detection. In Proceedings of the 19th international conference on World wide web (pp. 631-640). ACM.

Newman, M. E. (2003). The structure and function of complex networks. SIAM review, 45(2), 167-256.

Newman, M. E., & Girvan, M. (2004). Finding and evaluating community structure in networks. Physical review E, 69(2), 026113.

Newman, M. E. (2006). Modularity and community structure in networks.Proceedings of the National Academy of Sciences, 103(23), 8577-8582.

Nishikawa, T., &Motter, A. E. (2011). Discovering network structure beyond communities. Scientific Reports, 1, 151.

OldemarRodriguez R. with contributions from Olger Calderon and Roberto Zuniga (2014). RSDA: RSDA - R to Symbolic Data Analysis. R package version 1.2. http://CRAN.R-project.org/package=RSDA

Piccardi, C., Calatroni, L., & Bertoni, F. (2010). Communities in Italian corporate networks. Physica A: Statistical Mechanics and its Applications,389(22), 5247-5258.

Porter, M. A., Onnela, J. P., &Mucha, P. J. (2009). Communities in networks. Notices of the AMS, 56(9), 1082-1097.

Reichardt, J., & Bornholdt, S. (2006). Statistical mechanics of community detection. Physical Review E, 74(1), 016110.

Wasserman, S., & Faust, K. (1994). Social network analysis: Methods and applications (Vol. 8). Cambridge University Press.