## One Citation

On the Laplacian spread of digraphs

- Mathematics
- 2022

. In this article, we extend the notion of the Laplacian spread to simple directed graphs (digraphs) using the restricted numerical range. First, we provide Laplacian spread values for several…

## References

SHOWING 1-10 OF 19 REFERENCES

Laplacian Dynamics on General Graphs

- Computer ScienceBulletin of mathematical biology
- 2013

An unexpected equivalence between deterministic Laplacian dynamics and the master equations of continuous-time Markov processes is revealed, which allows rigorous treatment within the framework of stochastic, single-molecule mechanisms.

Matrix analysis

- MathematicsStatistical Inference for Engineers and Data Scientists
- 2018

This new edition of the acclaimed text presents results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications.

On the numerical range of a matrix

- Mathematics
- 2007

This is an English translation of the article “Uber den Wertevorrat einer Matrix” by Rudolf Kippenhahn, Mathematische Nachrichten 6 (1951), 193–228. This article is often cited by mathematicians who…

On the numerical range of a matrix

- Mathematics
- 2008

This is an English translation of the article “Über den Wertevorrat einer Matrix” by Rudolf Kippenhahn, Mathematische Nachrichten 6 (1951), 193–228. This article is often cited by mathematicians who…

Generalized algebraic connectivity for asymmetric networks

- Mathematics, Computer Science2016 American Control Conference (ACC)
- 2016

The notion of generalized algebraic connectivity is introduced for this type of network as an extension of conventionalgebraic connectivity measure for symmetric networks as a new notion represents the expected asymptotic convergence rate of a cooperative algorithm used to control the network.

Normal matrices

- Mathematics
- 2021

Let A be a square complex matrix and z a complex number. The distance, with respect to the spectral norm, from A to the set of matrices which have z as an eigenvalue is less than or equal to the…

NUMERICAL DETERMINATION OF THE FIELD OF VALUES OF A GENERAL COMPLEX MATRIX

- Mathematics
- 1978

For an $n \times n$ complex matrix A, the convexity of $F(A) \equiv \{ x^ * Ax:x^ * x = 1,x \in C^n \} $ and some simple observations are exploited to determine certain boundary points and tangents…

Topics in Matrix Analysis

- Mathematics
- 1991

1. The field of values 2. Stable matrices and inertia 3. Singular value inequalities 4. Matrix equations and Kronecker products 5. Hadamard products 6. Matrices and functions.

On the restricted numerical range of the Laplacian matrix for digraphs

- Mathematics
- 2020

ABSTRACT In this article, we present the restricted numerical for the Laplacian matrix of a directed graph (digraph). We motivate our interest in the restricted numerical range by its close…