Abstract
The development in network science shows various applications of network science concepts in different fields of research. Recently, the analysis using multilayer network has drawn attention of researchers for its multifaceted modeling framework. This paper discusses layer similarity in a multiplex network that is a special type of multilayer network. We investigate one of the recent approaches in layer similarity that uses cosine similarity as a neighborhood-based approach of defining node and layer similarity. We show the problem with the existing approach of similarity and introduce neighborhood-structural and neighborhood-spectral composition to explain node and layer similarity. In these compositions, we add structural and spectral discrepancies as penalty factor to neighborhood similarity. We use k-shell decomposition and eigenvector ranking to define structural and spectral importance, respectively. The final layer similarity combines both neighborhood-structural and neighborhood-spectral compositions to evaluate layer similarity. Like the existing approach, the proposed approach focuses on pair-wise layer similarity. The results show that there exist some differences in ranking pair-wise layer similarity between the proposed and exiting approach. A high degree of correlation is found between the proposed and existing approach. The proposed penalty factor captures the mismatch in ranking. The average accuracy of link prediction is found to be better in case of proposed approach than the existing approach.
Similar content being viewed by others
Data availability
The datasets analyzed during the current study are available in the https://manliodedomenico.com/data.php repository.
References
Bera BK, Rakshit S, Ghosh D (2019) Intralayer synchronization in neuronal multiplex network. Eur Phys J Spec Top. https://doi.org/10.1140/epjst/e2019-900007-8
Bjelland J, Burgess M, Canright G, Engø-Monsen K (2010) Eigenvectors of directed graphs and importance scores: dominance, T-Rank, and sink remedies. Data Min Knowl Disc. https://doi.org/10.1007/s10618-009-0154-1
Borgatti SP, Everett MG (2000) Models of core/periphery structures. Soc Netw. https://doi.org/10.1016/S0378-8733(99)00019-2
Bródka P, Chmiel A, Magnani M, Ragozini G (2018) Quantifying layer similarity in multiplex networks: a systematic study. R Soc Open Sci. https://doi.org/10.1098/rsos.171747
Carpi LC, Schieber TA, Pardalos PM, Marfany G, Masoller C, Díaz-Guilera A, Ravetti MG (2019) Assessing diversity in multiplex networks. Sci Rep. https://doi.org/10.1038/s41598-019-38869-0
De Domenico M, Lancichinetti A, Arenas A, Rosvall M (2015) Identifying modular flows on multilayer networks reveals highly overlapping organization in interconnected systems. Phys Rev X. https://doi.org/10.1103/PhysRevX.5.011027
Gómez S, Díaz-Guilera A, Gómez-Gardeñes J, Pérez-Vicente CJ, Moreno Y, Arenas A (2013) Diffusion dynamics on multiplex networks. Phys Rev Lett. https://doi.org/10.1103/PhysRevLett.110.028701
Gupta Y, Das D, Iyengar SRS (2016) Pseudo-cores: the terminus of an intelligent viral Meme’s trajectory. Stud Comput Intell. https://doi.org/10.1007/978-3-319-30569-1_16
Halu A, De Domenico M, Arenas A, Sharma A (2019) The multiplex network of human diseases. Npj Syst Biol Appl. https://doi.org/10.1038/s41540-019-0092-5
Huang Y, Dai H (2017) On information spreading in multiplex networks with gossip mechanism. IEEE Int Conf Commun. https://doi.org/10.1109/ICC.2017.7997367
Jalan S, Pradhan P (2018) Localization of multilayer networks by optimized single-layer rewiring. Phys Rev E. https://doi.org/10.1103/PhysRevE.97.042314
Kitsak M, Gallos LK, Havlin S, Liljeros F, Muchnik L, Stanley HE, Makse HA (2010) Identification of influential spreaders in complex networks. Nat Phys. https://doi.org/10.1038/nphys1746
Li L, Liu J (2020) The aggregation of multiplex networks based on the similarity of networks. Phys A Stat Mech Appl. https://doi.org/10.1016/j.physa.2019.122976
Liu Y, Tang M, Zhou T et al (2015) Improving the accuracy of the k-shell method by removing redundant links: from a perspective of spreading dynamics. Sci Rep 5:13172. https://doi.org/10.1038/srep13172
Liu H, Yang N, Yang Z, Lin J, Zhang Y (2020) The impact of firm heterogeneity and awareness in modeling risk propagation on multiplex networks. Phys A Stat Mech Appl. https://doi.org/10.1016/j.physa.2019.122919
Magnani M, Micenková B, & Rossi L (2013) Combinatorial analysis of multiple networks. arXiv:1303.4986 [cs.SI]
Newman MEJ (2010) Networks: an introduction. Oxford University Press, New York
Renoust B, Claver V, Baffier JF (2017) Multiplex flows in citation networks. Appl Netw Sci. https://doi.org/10.1007/s41109-017-0035-2
Stella M, Beckage NM, Brede M (2017) Multiplex lexical networks reveal patterns in early word acquisition in children. Sci Rep. https://doi.org/10.1038/srep46730
Walpole RE, Myers RH, Myers SL, Ye K (2007) Probability & statistics for engineers scientists. Pearsons Educ Int. https://doi.org/10.2307/2288012
Zhang RJ, Ye FY (2020) Measuring similarity for clarifying layer difference in multiplex ad hoc duplex information networks. J Informet. https://doi.org/10.1016/j.joi.2019.100987
Zhao DW, Wang LH, Zhi YF, Zhang J, Wang Z (2016) The robustness of multiplex networks under layer node-based attack. Sci Rep. https://doi.org/10.1038/srep24304
Funding
The author declares that he has no financial interests.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The author declares that he has no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Mohapatra, D. A hybrid approach for pair-wise layer similarity in a multiplex network. Soc. Netw. Anal. Min. 11, 88 (2021). https://doi.org/10.1007/s13278-021-00802-7
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s13278-021-00802-7