%0 Journal Article %1 AzimiTafreshi2014Giant %A Azimi-Tafreshi, N. %A Dorogovtsev, S. N. %A Mendes, J. F. F. %D 2014 %J Physical Review E %K percolation multiplex-networks directed-networks %N 5 %R 10.1103/PhysRevE.90.052809 %T Giant components in directed multiplex networks %U http://dx.doi.org/10.1103/PhysRevE.90.052809 %V 90 %X We describe the complex global structure of giant components in directed multiplex networks which generalizes the well-known bow-tie structure, generic for ordinary directed networks. By definition, a directed multiplex network contains vertices of one kind and directed edges of m different kinds. In directed multiplex networks, we distinguish a set of different giant components based on inter-connectivity of their vertices, which is understood as various directed paths running entirely through edges of distinct types. If, in particular, \$m = 2\$, we define a strongly viable component as a set of vertices, in which each two vertices are interconnected by two pairs of directed paths, running through edges of each of two kinds in both directions. We show that in this case, a directed multiplex network contains, in total, 9 different giant components including the strongly viable component. In general, the total number of giant components is \$3^m\$. For uncorrelated directed multiplex networks, we obtain exactly the size and the birth point of the strongly viable component and estimate the sizes of other giant components.

@article{AzimiTafreshi2014Giant, abstract = {{We describe the complex global structure of giant components in directed multiplex networks which generalizes the well-known bow-tie structure, generic for ordinary directed networks. By definition, a directed multiplex network contains vertices of one kind and directed edges of m different kinds. In directed multiplex networks, we distinguish a set of different giant components based on inter-connectivity of their vertices, which is understood as various directed paths running entirely through edges of distinct types. If, in particular, \$m = 2\$, we define a strongly viable component as a set of vertices, in which each two vertices are interconnected by two pairs of directed paths, running through edges of each of two kinds in both directions. We show that in this case, a directed multiplex network contains, in total, 9 different giant components including the strongly viable component. In general, the total number of giant components is \$3^m\$. For uncorrelated directed multiplex networks, we obtain exactly the size and the birth point of the strongly viable component and estimate the sizes of other giant components.}}, added-at = {2019-06-10T14:53:09.000+0200}, archiveprefix = {arXiv}, author = {Azimi-Tafreshi, N. and Dorogovtsev, S. N. and Mendes, J. F. F.}, biburl = {https://www.bibsonomy.org/bibtex/2be830932ee56eb753530723ffdbc27cc/nonancourt}, citeulike-article-id = {13268815}, citeulike-linkout-0 = {http://dx.doi.org/10.1103/PhysRevE.90.052809}, citeulike-linkout-1 = {http://arxiv.org/abs/1407.4623}, citeulike-linkout-2 = {http://arxiv.org/pdf/1407.4623}, day = 17, doi = {10.1103/PhysRevE.90.052809}, eprint = {1407.4623}, interhash = {b92e0c3eea20a5b96f301804e73e7891}, intrahash = {be830932ee56eb753530723ffdbc27cc}, issn = {1550-2376}, journal = {Physical Review E}, keywords = {percolation multiplex-networks directed-networks}, month = nov, number = 5, posted-at = {2014-07-18 09:59:17}, priority = {2}, timestamp = {2019-09-24T18:00:53.000+0200}, title = {{Giant components in directed multiplex networks}}, url = {http://dx.doi.org/10.1103/PhysRevE.90.052809}, volume = 90, year = 2014 }