Abstract
This chapter considers graph partition of a particular kind of complex networks referred to as power law graphs. In particular, we focus our analysis on the market graph, constructed from time series of price return on the American stock market. Two different methods originating from clustering analysis in social networks and image segmentation are applied to obtain graph partitions and the results are evaluated in terms of the structure and quality of the partition. Our results show that the market graph possesses a clear clustered structure only for higher correlation thresholds. By studying the internal structure of the graph clusters we found that they could serve as an alternative to traditional sector classification of the market. Finally, partitions for different time series were considered to study the dynamics and stability in the partition structure. Even though the results from this part were not conclusive we think this could be an interesting topic for future research.
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Appendix
Appendix
Number of runs is N = 50
1.1 Adjusted Rand Index
ARI for different partition approaches and market graphs. The ARI was obtained by choosing three pairs of partitions, at random from each type, computing the ARI for each of them, and then taking the average of these values. (GM—greedy modularity, SNC—spectral normalized cut.)
1.2 Industrial Sectors in the Market Graph
1.3 Industrial Sectors and Clusters
Market graph θ = 0. 5 with industrial sectors and clusters from greedy modularity. The italic numbers represent the largest sector in every cluster.
Market graph θ = 0. 7 with industrial sectors and clusters from greedy modularity.
Partitions of market graph for different periods.
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Sörensen, K., Pardalos, P.M. (2016). Clustering in Financial Markets. In: Kalyagin, V., Koldanov, P., Pardalos, P. (eds) Models, Algorithms and Technologies for Network Analysis. NET 2014. Springer Proceedings in Mathematics & Statistics, vol 156. Springer, Cham. https://doi.org/10.1007/978-3-319-29608-1_16
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