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Questions tagged [weighted-graphs]

Questions about graphs in which every edge is associated with a weight.

395 questions
62
votes
5 answers

Is zero allowed as an edge's weight, in a weighted graph?

I am trying to write a script that generates random graphs and I need to know if an edge in a weighted graph can have the 0 value. actually it makes sense that 0 could be used as an edge's weight, but I've been working with graphs in last few days…
Taxellool
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3 answers

Why does Dijkstra's algorithm fail on a negative weighted graphs?

I know this is probably very basic, I just can't wrap my head around it. We recently studied about Dijkstra's algorithm for finding the shortest path between two vertices on a weighted graph. My professor said this algorithm will not work on a graph…
so.very.tired
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29
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3 answers

When is the minimum spanning tree for a graph not unique

Given a weighted, undirected graph G: Which conditions must hold true so that there are multiple minimum spanning trees for G? I know that the MST is unique when all of the weights are distinct, but you can't reverse this statement. If there are…
Keiwan
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22
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2 answers

Do the minimum spanning trees of a weighted graph have the same number of edges with a given weight?

If a weighted graph $G$ has two different minimum spanning trees $T_1 = (V_1, E_1)$ and $T_2 = (V_2, E_2)$, then is it true that for any edge $e$ in $E_1$, the number of edges in $E_1$ with the same weight as $e$ (including $e$ itself) is the same…
Aden Dong
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20
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6 answers

Real life examples of negative weight edges in graphs

I am unable to relate to any real life examples of negative weight edges in graphs. Distances between cities cannot be negative. Time taken to travel from one point to another cannot be negative. Data transfer rates cannot be negative. I am just…
Sandeep
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15
votes
2 answers

Shortest non intersecting path for a graph embedded in a euclidean plane (2D)

What algorithm would you use to find the shortest path of a graph, which is embedded in an euclidean plane, such that the path should not contain any self-intersections (in the embedding)? For example, in the graph below, you want to go from $(0,0)…
Realz Slaw
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12
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3 answers

Modifying Dijkstra's algorithm for edge weights drawn from range $[1,…,K]$

Suppose I have a directed graph with edge weights drawn from range $[1,\dots, K]$ where $K$ is constant. If I'm trying to find the shortest path using Dijkstra's algorithm, how can I modify the algorithm / data structure and improve the time…
user1675999
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12
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0 answers

Optimal meeting point in directed graph

Let $G(V, E)$ be a edge-weighted directed connected graph and $v_1, \dots, v_n \in V$ be some vertices. Let $d(a, b)$ denote the length of the shortest path from $a$ to $b$, for $a,b \in V$. I need to find a vertex $v \in V$ such that $$\sum_{i=1}^n…
vojta
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11
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0 answers

Minimum edge deletion partitioning of a planar graph

I'm interested in the time complexity of the following problem: Given an undirected planar graph $G=(V,E)$ and a weight function $w:E \rightarrow \mathbb{Z}$ (so weights can be negative, too), color the vertices in such a way that the sum of the…
EmreA
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9
votes
1 answer

Minimum s-t cut in weighted directed acyclic graphs with possibly negative weights

I ran into the following problem: Given a directed acyclic graph with real-valued edge weights, and two vertices s and t, compute the minimum s-t cut. For general graphs this is NP-hard, since one can trivially reduce max-cut to it by simply…
George
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9
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2 answers

What are Markov chains?

I'm currently reading some papers about Markov chain lumping and I'm failing to see the difference between a Markov chain and a plain directed weighted graph. For example in the article Optimal state-space lumping in Markov chains they provide the…
Bakuriu
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9
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2 answers

An edge that connects more than two nodes in a graph?

Is there a way to create a single edge on a graph that connects 3 or more nodes? For example, let's say that the probability of Y occurring after X is 0.1, and the probability of Z occurring after Y is 0.001, but the probability of Z occurring after…
Nick Anderegg
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9
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11 answers

Real life examples of *zero* weight edges in graphs

The meaning of edges with zero weight in a weighted graph questions me for a long time, and I even asked a related question previously. Yet, when I recently read here a question on real life example of graphs with negative weight edges I was amazed…
Matthieu Latapy
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9
votes
1 answer

Shortest Path in a Directed Acyclic Graph with two types of costs

I am given a directed acyclic graph $G = (V,E)$, which can be assumed to be topologically ordered (if needed). Each edge $e$ in G has two types of costs - a nominal cost $w(e)$ and a spiked cost $p(e)$. I am also given two nodes in $G$, node $s$ and…
Miel Sharf
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9
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1 answer

Effect of increasing the capacity of an edge in a flow network with known max flow

I need your help with an exercise on Ford-Fulkerson. Suppose you are given a flow network with capacities $(G,s,t)$ and you are also given the max flow $|f|$ in advance. Now suppose you are given an arc $e$ in $G$ and suppose this arc's capacity is…
SyndicatorBBB
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