### Abstract

The second smallest eigenvalue of the Laplacian matrix, also known as the algebraic connectivity, characterizes the performance of some dynamic processes on networks, such as consensus in multiagent networks, synchronization of coupled oscillators, random walks on graphs, and so on. In a multiagent network, for example, the larger the algebraic connectivity of the graph representing interactions between agents is, the faster the convergence speed of a representative consensus algorithm is. This paper tackles the problem of finding graphs that maximize or locally maximize the algebraic connectivity in the space of graphs with a fixed number of vertices and edges. It is shown that some well-known classes of graphs such as star graphs, cycle graphs, complete bipartite graphs and circulant graphs are algebraic connectivity maximizers or local maximizers under certain conditions.

Original language | English |
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Article number | 7336529 |

Journal | IEEE Transactions on Control of Network Systems |

Volume | PP |

Issue number | 99 |

DOIs | |

Publication status | Published - 2015 |

### Keywords

- Algebraic connectivity
- Consensus algorithm
- Convergence rate
- Laplacian matrix
- Multiagent network

### ASJC Scopus subject areas

- Control and Systems Engineering
- Signal Processing
- Computer Networks and Communications
- Control and Optimization

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## Cite this

*IEEE Transactions on Control of Network Systems*,

*PP*(99), [7336529]. https://doi.org/10.1109/TCNS.2015.2503561