Application of hyperbolic geometry of multiplex networks under layer link-based attacks

As real multilayer networks, we consider four networks. The multilayer networks are converted to multiplex networks by assuming that all layers have the same number of nodes (the maximum number of nodes of all layers). Explanation of these networks is as follow: <em>CS-Aarhus_multiplex [1]</em> : The first network used in this study is a 5-layer multiplex network, named CS-Aarhus_multiplex, which has 61 nodes and 620 edges. The multiplex social network consists of five kinds of online and offline relationships (Facebook, Leisure, Work, Co-authorship, Lunch) between the employees of the Computer Science department at Aarhus. <em>Data_malaria_PLOSCompBiology_2013 [2]</em>: The second network is a 9-layer multiplex network, which consists of 307 nodes and 35306 edges. Networks of recombinant antigen genes from the human malaria parasite P. falciparum. Each of the 9 networks shares the same set of vertices but has different edges, corresponding to the 9 highly variable regions (HVRs) in the DBLa domain of the var protein. Nodes are var genes, and two genes are connected if they share a substring whose length is statistically significant. VICKERS CHAN 7th-GRADERS [3] : The third network is a 3-layer multiplex network, called VICKERS CHAN 7th-GRADERS, which includes 29 nodes and 740 edges. The data were collected by Vickers from 29 seventh-grade students in a school in Victoria, Australia. Students were asked to nominate their classmates on several relations including the three layers. 4. FAO MULTIPLEX TRADE NETWORK [4]: The fourth network is a 364-layer multiplex network, which contains 214 nodes and 318346 edges. We consider different types of trade relationships among countries, obtained from FAO (Food and Agriculture Organization of the United Nations)