### Abstract

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:fi rst, 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.

Original language | English (US) |
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Title of host publication | SIGMETRICS 2018 - Abstracts of the 2018 ACM International Conference on Measurement and Modeling of Computer Systems |

Publisher | Association for Computing Machinery, Inc |

Pages | 119-121 |

Number of pages | 3 |

ISBN (Electronic) | 9781450358460 |

DOIs | |

State | Published - Jun 12 2018 |

Event | 2018 ACM International Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 2018 - Irvine, United States Duration: Jun 18 2018 → Jun 22 2018 |

### Publication series

Name | SIGMETRICS 2018 - Abstracts of the 2018 ACM International Conference on Measurement and Modeling of Computer Systems |
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### Conference

Conference | 2018 ACM International Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 2018 |
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Country | United States |

City | Irvine |

Period | 6/18/18 → 6/22/18 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Networks and Communications
- Hardware and Architecture
- Computational Theory and Mathematics
- Software

### Cite this

*SIGMETRICS 2018 - Abstracts of the 2018 ACM International Conference on Measurement and Modeling of Computer Systems*(pp. 119-121). (SIGMETRICS 2018 - Abstracts of the 2018 ACM International Conference on Measurement and Modeling of Computer Systems). Association for Computing Machinery, Inc. https://doi.org/10.1145/3219617.3219667

**On a class of stochastic multilayer networks.** / Jiang, Bo; Towsley, Don; Nain, Philippe; Guha, Saikat.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*SIGMETRICS 2018 - Abstracts of the 2018 ACM International Conference on Measurement and Modeling of Computer Systems.*SIGMETRICS 2018 - Abstracts of the 2018 ACM International Conference on Measurement and Modeling of Computer Systems, Association for Computing Machinery, Inc, pp. 119-121, 2018 ACM International Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 2018, Irvine, United States, 6/18/18. https://doi.org/10.1145/3219617.3219667

}

TY - GEN

T1 - On a class of stochastic multilayer networks

AU - Jiang, Bo

AU - Towsley, Don

AU - Nain, Philippe

AU - Guha, Saikat

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:fi rst, 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:fi rst, 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.

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U2 - 10.1145/3219617.3219667

DO - 10.1145/3219617.3219667

M3 - Conference contribution

AN - SCOPUS:85050373083

T3 - SIGMETRICS 2018 - Abstracts of the 2018 ACM International Conference on Measurement and Modeling of Computer Systems

SP - 119

EP - 121

BT - SIGMETRICS 2018 - Abstracts of the 2018 ACM International Conference on Measurement and Modeling of Computer Systems

PB - Association for Computing Machinery, Inc

ER -