# Questions tagged [graph-distance]

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19
questions

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### Does exponential degree distribution entail Log-normal distance distribution in large complex graphs?

We've been exploring the graph structure of a large genealogical data base (WikiTree) of which main connected component contains about 23 million nodes. The graph edges are defined by any direct ...

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134 views

### Finding a tree with adjacency matrix near a given matrix

For defining a distance between trees, one can code them into $\mathbb{R}^n$ and use norms in $\mathbb{R}^n$ as distance. (For example we can use adjacency matrices as a tool for this coding) After ...

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116 views

### "Arc" length parametrization for surfaces

If we have a function $\phi:\Omega\subseteq\mathbb{R}^2\to\mathbb{R}$, $\phi\in C^2(\Omega)$ is there a way to find a function $d:\Omega\to\mathbb{R}, d\in C^2(\Omega)$ so that:
$|\nabla d(x,y)|=1,\ \...

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36 views

### Antipodal vertices in spectral graph embeddings

Suppose your are given an antipodal graph $G=(V,E)$, that is, for every vertex $v\in V$ there is a unique maximally distant vertex $v'\in V$.
Under which condistions does the following hold:
If $\...

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**1**answer

67 views

### Distance pairs in labeled directed graph

Suppose we have a simple directed graph with $n$ nodes and $m$ edges, and we label each edge from $1$ to $m$ (with distinct labels). Define the weighted "length" of a directed path to be the maximum ...

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115 views

### Voronoi diagram on (weighted) graphs

Suppose I have a graph $G$ (possibly with weights on edges), and I have a subset $S$ of $k$ vertices $s_1, \dotsc, s_k$. I want to solve the post office problem: that is, I want to partition the ...

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165 views

### Distance function and its approximation

An easy and quick question:
Consider a function $u\in C(\Omega)$, where $\Omega$ is a bounded domain in $\mathbb{R}^n$.
Define a function $Q$ that measures the distance of a point $(x,y) \in\mathbb{...

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**1**answer

86 views

### Distance between two polyhedra that takes incidence structure into account

Suppose that we have two polyhedra $P_1$ and $P_2$ in $\mathbb{R}^3$. I would like to define such a metric $\rho(P_1, P_2)$ that depends on several factors, but currently I don't know how to do it ...

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435 views

### Graph contained in a metric space

I have a metric space $X$ and a graph $G=(V,E)$ whose set of vertices is a subset $V\subset X$ (and $E$ is the set of edges, which is a symmetric subset of $V\times V$). For each $v\in V$, the set of ...

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954 views

### Finding the farthest point from a set of other points

I have a set of nodes in a very large graph which I call Cluster Points. I also have for each point in the graph, the distance from each point in the Cluster point set.
For example: ...

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3k views

### Is the Haversine Formula or the Vincenty's Formula better for calculating distance?

Which is better for calculating the distance between two latitude/longitude points, The Haversine Formula or The Vincenty's Formula? Why?
The distance is obviously being calculated on Earth. Does ...

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293 views

### Edit distance vs. canonical adjacency matrix distance

Let $G$ and $G'$ be two simple random graphs on the same set of nodes. Let $d_{edit}$ be the edit distance between $G$ and $G'$. Let $\mathbf{A}$ and $\mathbf{A'}$ be the adjacency matrices of the ...

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136 views

### Of the standard distance metrics, which ones can/cannot be embedded in Euclidean space?

Given the discussion from:
Representability of finite metric spaces
it appears that a 1974 paper by Morgan gives the criteria for when a distance metric can be embedded in Euclidean space. My first ...

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2k views

### Possible ways to create a graph representation from a distance matrix (through approximation)

Forgive me, Im not math professional, but a computer scientist at the beginning of my base research from my thesis, so bare with me if I miss something blatantly obvious.
I have a Euclidean distance ...

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71 views

### Looking for similar centrality measurement on graph

I'm working on a graph problem somehow related to centrality measurement. Given an undirected, unweighted tree $T$ and a vertex $v$, let $D_i(v)$ be the set of vertices in $T$ that are i hops from $v$,...

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192 views

### planar bipartite cubic graph

Suppose we have a cubic planar bipartite graph with no double edges. I am looking for a statement about the minimal distance between the square faces (shortest path from a vertex on the first square ...

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3k views

### Distance between two networks

Suppose you have networks A and B, each with a set of nodes and edges. You want to measure how similar the networks are to each-other. None of the nodes or edges are labelled. What are the metric(s) ...

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**1**answer

258 views

### Graphs with circulant distance matrices

The cycle has this property. For instance, the distance matrix for a 6-cycle is:
$A=\begin{bmatrix}
0 & 1 & 2 & 3 & 2 & 1 \\\\
1 & 0 & 1 &...

**3**

votes

**2**answers

395 views

### Graphs with a unique transmission value

If $G$ is a graph with distance function $d(x,y)$ between vertices, the transmission of a vertex $x \in v(G)$ is defined as $\sigma_{x}=\sum_{y \neq x}{d(x,y)}$. I want to know if there is a known ...