Algebraic connectivity of directed graphs

By Chai Wah Wu. 2005

169 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/36f9765725c854d316324412d49483ddad5c646d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

1. S. E. Tuna
2. Frank Allgöwer
3. Jorge Cortés
4. Bahman Gharesifard
5. Luca Scardovi
6. Peter Wieland
7. Jung-Su Kim
8. Murat Arcak

In Geometry and Topology

1. Jorge Cortés
2. Murat Arcak
3. S. E. Tuna
4. Bahman Gharesifard

In Statistical and Nonlinear Physics

1. Frank Allgöwer
2. Jorge Cortés
3. Murat Arcak
4. Frank Schweitzer
5. S. E. Tuna
6. Bahman Gharesifard

Citations in the corpus

• When does a digraph admit a doubly stochastic adjacency matrix? (2010, background): “8, note that even if connectivity is preserved, fewer edges lead to smaller algebraic connectivity [20], which in turn affects negatively the rate of convergence of the consensus, optimization, and gossip algorithms executed over doubly stochastic digraphs, see e.”
• LQR-based coupling gain for synchronization of linear systems (2008, methodology): “into which the problem studied in this note falls, has also accommodated important theoretical developments especially by using tools from algebraic graph theory [27].”
• Synchronization of Interconnected Systems With Applications to Biochemical Networks: An Input-Output Approach (2009, background): “The connectivity properties of the corresponding graphs are related to the algebraic properties of the Laplacian matrices and, in particular, to the notion of algebraic connectivity extended to directed graphs in [17]: Definition 1: For a directed graph with Laplacian matrix , the algebraic connecti”
• On consensus in multi-agent systems with linear high-order agents (2008, background): “If G is balanced, the algebraic connectivity satisfies 0 ≤ a(G) ≤ Re(λ2(L)), where λ2(L) is the eigenvalue of L with the second smallest real part, and a(G) > 0 if and only if G is connected (cf. Wu (2005)).”
• Causality-driven slow-down and speed-up of diffusion in non-Markovian temporal networks (2013, background): “Its magnitude has been shown to reflect how “well-connected” a network is and whether its topology exhibits small cuts [27, 28].”
• Conditions for Synchronizability in Arrays of Coupled Linear Systems (2008, background): “The second case has also accommodated important theoretical developments especially by the use of tools from algebraic graph theory [30].”