Abstract
Graphs often model complex phenomena in diverse fields, such as social networks, connectivity among brain regions, or protein-protein interactions. However, standard computational methods are insufficient for empirical network analysis due to randomness. Thus, a natural solution would be the use of statistical approaches. A recent paper by Takahashi et al. suggested that the graph spectrum is a good fingerprint of the graph’s structure. They developed several statistical methods based on this feature. These methods, however, rely on the distribution of the eigenvalues of the graph being real-valued, which is false when graphs are directed. In this paper, we extend their results to directed graphs by analyzing the distribution of complex eigenvalues instead. We show the strength of our methods by performing simulations on artificially generated groups of graphs and finally show a proof of concept using concrete biological data obtained by Project Tycho.
This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001.
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References
Alon, U.: An Introduction to Systems Biology: Design Principles of Biological Circuits. Chapman & Hall/CRC Mathematical and Computational Biology (2006)
Barabasi, A.L., Oltvai, Z.N.: Network biology: understanding the cell’s functional organization. Nat. Rev. Genet. 5, 101–113 (2004)
Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)
Bullmore, E., Sporns, O.: Complex brain networks: graph theoretical analysis of structural and functional systems. Nat. Rev. Neurosci. 10, 186–198 (2009)
Csardi, G., Nepusz, T.: The igraph software package for complex network research. Interjournal Complex Syst. 1695 (2006)
Duong, T.: KS: kernel density estimation and kernel discriminant analysis for multivariate data in R. J. Stat. Softw. 21(7), 1–16 (2007)
Erdős, P., Rényi, A.: On random graphs I. Publ. Math. Debrecen 6, 290–297 (1959)
Freeman, L.: A set of measures of centrality based on betweenness. Sociometry 40, 35–41 (1977)
Fujita, A., Vidal, M.C., Takahashi, D.Y.: A statistical method to distinguish functional brain networks. Front. Neurosci. 11, 66 (2017)
Fujita, A., Silva Lira, E., De Siqueira Santos, S.: A semi-parametric statistical test to compare complex networks. J. Complex Netw. 8 (2020)
Fujita, A., Takahashi, D.Y., Balardin, J.B., Vidal, M.C., Sato, J.R.: Correlation between graphs with an application to brain network analysis. Comput. Stat. Data Anal. 109, 76–92 (2017)
Lees-miller, J., et al.: Correlation between graphs with an application to brain network analysis. Comput. Stat. Data Anal. 109, 76–92 (2017)
MacKay, D.J.: Information Theory, Inference, and Learning Algorithms, 1st edn. Cambridge University Press, Cambridge (2003)
Ramos, T.C., Mourão-Miranda, J., Fujita, A.: Spectral density-based clustering algorithms for complex networks. Front. Neurosci. 17, 926321 (2023)
Ribeiro, A., Vidal, M., Sato, J., Fujita, A.: Granger causality among graphs and application to functional brain connectivity in autism spectrum disorder. Entropy 23, 1204 (2021)
Sameshima, K., Baccala, L.: Methods in brain connectivity inference through multivariate time series analysis (2016)
Santos, S.S., Fujita, A.: statGraph: statistical methods for graphs (2017). www.cran.r-project.org/package=statGraph
Scott, J.: Social Network Analysis. Sage, Newcastle upon Tyne (2012)
Watts, D., Strogatz, S.: Collective dynamics of “small-world’ networks. Nature 393, 440–442 (1998)
Yanagawa, T., Chao, Z.C., Hasegawa, N., Fujii, N.: Large-scale information flow in conscious and unconscious states: an ECoG study in monkeys. PLoS ONE 8(11), e80845 (2013)
Acknowledgements
This work has been supported by FAPESP grants 2018/21934-5, 2019/22845-9, and 2020/08343-8, CNPq grant 303855/2019-3 and 440245/2022-2, CAPES (finance code 001), Alexander von Humboldt Foundation, the Academy of Medical Sciences - Newton Fund, and Wellcome Leap.
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Villela, V.C., Lira, E.S., Fujita, A. (2023). Spectrum-Based Statistical Methods for Directed Graphs with Applications in Biological Data. In: Reis, M.S., de Melo-Minardi, R.C. (eds) Advances in Bioinformatics and Computational Biology. BSB 2023. Lecture Notes in Computer Science(), vol 13954. Springer, Cham. https://doi.org/10.1007/978-3-031-42715-2_5
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