TY - JOUR
T1 - On a Class of Stochastic Multilayer Networks
AU - Jiang, Bo
AU - Nain, Philippe
AU - Towsley, Don
AU - Guha, Saikat
N1 - Funding Information:
This research was supported in part by the U.S. National Science Foundation under Grant Number CNS-1413998, and by the U.S. Army Research Laboratory and the U.K. Ministry of Defence under Agreement Number W911NF-16-3-0001.
Publisher Copyright:
© 2018 ACM.
PY - 2018/6/12
Y1 - 2018/6/12
N2 - In this paper, we introduce a new class of stochastic multilayer networks. A stochastic multilayer network is the aggregation of M networks (one per layer) where each is a subgraph of a foundational network G . Each layer network is the result of probabilistically removing links and nodes from G . The resulting network includes any link that appears in at least K layers. This model is an instance of a non-standard site-bond percolation model. Two sets of results are obtained: first, we derive the probability distribution that the M -layer network is in a given configuration for some particular graph structures (explicit results are provided for a line and an algorithm is provided for a tree), where a configuration is the collective state of all links (each either active or inactive). Next, we show that for appropriate scalings of the node and link selection processes in a layer, links are asymptotically independent as the number of layers goes to infinity, and follow Poisson distributions. Numerical results are provided to highlight the impact of having several layers on some metrics of interest (including expected size of the cluster a node belongs to in the case of the line). This model finds applications in wireless communication networks with multichannel radios, multiple social networks with overlapping memberships, transportation networks, and, more generally, in any scenario where a common set of nodes can be linked via co-existing means of connectivity.
AB - In this paper, we introduce a new class of stochastic multilayer networks. A stochastic multilayer network is the aggregation of M networks (one per layer) where each is a subgraph of a foundational network G . Each layer network is the result of probabilistically removing links and nodes from G . The resulting network includes any link that appears in at least K layers. This model is an instance of a non-standard site-bond percolation model. Two sets of results are obtained: first, we derive the probability distribution that the M -layer network is in a given configuration for some particular graph structures (explicit results are provided for a line and an algorithm is provided for a tree), where a configuration is the collective state of all links (each either active or inactive). Next, we show that for appropriate scalings of the node and link selection processes in a layer, links are asymptotically independent as the number of layers goes to infinity, and follow Poisson distributions. Numerical results are provided to highlight the impact of having several layers on some metrics of interest (including expected size of the cluster a node belongs to in the case of the line). This model finds applications in wireless communication networks with multichannel radios, multiple social networks with overlapping memberships, transportation networks, and, more generally, in any scenario where a common set of nodes can be linked via co-existing means of connectivity.
KW - percolation
KW - stochastic multilayer network
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U2 - 10.1145/3219617.3219667
DO - 10.1145/3219617.3219667
M3 - Article
AN - SCOPUS:85084179410
VL - 46
SP - 119
EP - 121
JO - Performance Evaluation Review
JF - Performance Evaluation Review
SN - 0163-5999
IS - 1
ER -