# Questions tagged [adjacency-matrices]

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10
questions

**2**

votes

**2**answers

149 views

### Adjacency matrix of total graph

Is there a nice way of relating the adjacency, incidence , Laplacian matrices and other matrices associated to a graph of a total graph with its original graph, or, say, at least relating that of the ...

**5**

votes

**1**answer

288 views

### Determining the primitive order of a binary matrix

Let ${\bf A}_n$ be an $2n \times 2n$ matrix that is defined as follows
$$
{\bf A}_n=\left(
\begin{array}{c}
0&0&\cdots&0&0&0&0&1&1\\
0&0&\cdots&0&0&...

**2**

votes

**1**answer

139 views

### When does a row standardized adjacency matrix have a real spectrum?

A colleague in spatial statistics was looking at a map with about 600 regions. For the application she's considering, the induced adjacency matrix had some undesirable properties (where two regions ...

**3**

votes

**1**answer

443 views

### Finding an adjacency matrix whose cube's diagonal is equal to a given vector

How can I find all binary matrices $A$ such that $A^3$ is a non-negative, integer square matrix and
$$\mbox{diag}\left(A^3\right)=b$$
for some given vector $b$?
Is there a way to characterize all ...

**10**

votes

**1**answer

446 views

### is it possible to have two non-isomorphic non-regular graphs with the same adjacent spectrum and the same laplacian spectrum?

For two regular graphs $G$ and $H$, it is possible for them to share the same adjacent spectrum and the same laplacian spectrum. While, on the other hand, is it possible to have two non-regular graphs ...

**1**

vote

**0**answers

101 views

### Primitivity of $AA^\top$

Let $A\in\mathbb{R}^{n\times n}$ be a non-negative and irreducible matrix. Consider $B:=AA^\top$. It can be proved (I can post a proof if needed) that the following condition is necessary and ...

**2**

votes

**0**answers

135 views

### Which functions preserve the connectivity of graphs/components?

I am somewhat stuck working on an issue and would really love some guidance. I will state the problem, my current state and what led to it in case the solution lies beyond where I was looking
The ...

**0**

votes

**2**answers

136 views

### Is there a name for this operation on graphs - e.g. duplication, Kronecker product of graphs?

I am revising a paper where one of the operations performed on a undirected graph with no loops, is to take each vertex, and split it into two vertices, and take each edge and replace it with 4 edges: ...

**-3**

votes

**1**answer

298 views

### adjacency matrix of random geometric graphs [closed]

Consider a graph with N nodes. All nodes are distributed as a Poisson point process with density of λ in a L*L area. There is an edge between two nodes if and only if the distance between them is less ...

**1**

vote

**1**answer

213 views

### power bounded adjacency matrices

A bounded linear operator $T$ on a Banach space $X$ is called power bounded if $\|T^k\|\le M$ for some $M>0$ and all $k\in \mathbb N$.
A classical result of Lorch says that if $X$ is reflexive, ...