k-core structure of real multiplex networks
Journal
Physical Review Research
Date Issued
July 2020
DOI
10.1103/PhysRevResearch.2.023176
Abstract
Multiplex networks are convenient mathematical representations for many real-world—biological, social,
and technological—systems of interacting elements, where pairwise interactions among elements have different flavors. Previous studies pointed out that real-world multiplex networks display significant interlayer
correlations—degree-degree correlation, edge overlap, node similarities—able to make them robust against
random and targeted failures of their individual components. Here, we show that interlayer correlations are
important also in the characterization of their k-core structure, namely, the organization in shells of nodes with
an increasingly high degree. Understanding of k-core structures is important in the study of spreading processes
taking place on networks, as for example in the identification of influential spreaders and the emergence of
localization phenomena. We find that, if the degree distribution of the network is heterogeneous, then a strong
k-core structure is well predicted by significantly positive degree-degree correlations. However, if the network
degree distribution is homogeneous, then strong k-core structure is due to positive correlations at the level of
node similarities. We reach our conclusions by analyzing different real-world multiplex networks, introducing
novel techniques for controlling interlayer correlations of networks without changing their structure, and taking
advantage of synthetic network models with tunable levels of interlayer correlations.
and technological—systems of interacting elements, where pairwise interactions among elements have different flavors. Previous studies pointed out that real-world multiplex networks display significant interlayer
correlations—degree-degree correlation, edge overlap, node similarities—able to make them robust against
random and targeted failures of their individual components. Here, we show that interlayer correlations are
important also in the characterization of their k-core structure, namely, the organization in shells of nodes with
an increasingly high degree. Understanding of k-core structures is important in the study of spreading processes
taking place on networks, as for example in the identification of influential spreaders and the emergence of
localization phenomena. We find that, if the degree distribution of the network is heterogeneous, then a strong
k-core structure is well predicted by significantly positive degree-degree correlations. However, if the network
degree distribution is homogeneous, then strong k-core structure is due to positive correlations at the level of
node similarities. We reach our conclusions by analyzing different real-world multiplex networks, introducing
novel techniques for controlling interlayer correlations of networks without changing their structure, and taking
advantage of synthetic network models with tunable levels of interlayer correlations.
File(s)![Thumbnail Image]()
![Thumbnail Image]()
Name
SM.pdf
Size
14.83 MB
Format
Adobe PDF
Checksum (MD5)
4a314060c2d1139c2929d652e0435d81
Name
PhysRevResearch.2.023176.pdf
Size
2.3 MB
Format
Adobe PDF
Checksum (MD5)
fa29eb07007eda3179ae6e8af9a5cc93