### Abstract

A distributed algorithm to compute the spectral radius of the graph in the presence of additive channel noise is proposed. The spectral radius of the graph is the eigenvalue with the largest magnitude of the adjacency matrix, and is a useful characterization of the network graph. Conventionally, centralized methods are used to compute the spectral radius, which involves eigenvalue decomposition of the adjacency matrix of the underlying graph. We devise an algorithm to reach consensus on the spectral radius of the graph using only local neighbor communications, both in the presence and absence of additive channel noise. The algorithm uses a distributed max update to compute the growth rate in the node state values and then performs a specific update to converge on the logarithm of the spectral radius. The algorithm works for any connected graph structure. Simulation results supporting the theory are also presented.

Original language | English (US) |
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Title of host publication | Conference Record - 53rd Asilomar Conference on Circuits, Systems and Computers, ACSSC 2019 |

Editors | Michael B. Matthews |

Publisher | IEEE Computer Society |

Pages | 1506-1510 |

Number of pages | 5 |

ISBN (Electronic) | 9781728143002 |

DOIs | |

State | Published - Nov 2019 |

Event | 53rd Asilomar Conference on Circuits, Systems and Computers, ACSSC 2019 - Pacific Grove, United States Duration: Nov 3 2019 → Nov 6 2019 |

### Publication series

Name | Conference Record - Asilomar Conference on Signals, Systems and Computers |
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Volume | 2019-November |

ISSN (Print) | 1058-6393 |

### Conference

Conference | 53rd Asilomar Conference on Circuits, Systems and Computers, ACSSC 2019 |
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Country | United States |

City | Pacific Grove |

Period | 11/3/19 → 11/6/19 |

### Keywords

- consensus
- distributed networks
- spectral radius
- Wireless sensor network

### ASJC Scopus subject areas

- Signal Processing
- Computer Networks and Communications

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## Cite this

*Conference Record - 53rd Asilomar Conference on Circuits, Systems and Computers, ACSSC 2019*(pp. 1506-1510). [9049018] (Conference Record - Asilomar Conference on Signals, Systems and Computers; Vol. 2019-November). IEEE Computer Society. https://doi.org/10.1109/IEEECONF44664.2019.9049018