Questions tagged [graph-distance]

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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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1answer
90 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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1answer
89 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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1answer
69 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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0answers
363 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 ...
3
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1answer
719 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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1answer
2k 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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0answers
286 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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0answers
130 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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0answers
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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0answers
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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1answer
189 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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3answers
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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1answer
234 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
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2answers
379 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 ...