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Questions tagged [subgraphs]

20 questions
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1 answer

Largest isomorphic subgraphs of two graphs with features

the following question came up in a problem I am working on: Suppose you have two graphs $G_1=(V_1, E_1), G_2=(V_2,E_2)$ that have features attached to them, i.e. to every $v\in V_1$ or $v\in V_2$ there is a vector $w_v\in\mathbb R^n$ with fixed $n$…
Tobias Kietreiber
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2 answers

Maximum planar subgraph problem

Given a graph G I want to find the maximum planar subgraph which is a grid graph. (Because the nodes of this subgraph represent points on a grid). Is there any library in python for finding the maximum planar subgraph? Is there some way how to…
nuemlouno
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3
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1 answer

Minimum number of groups such that every element in graph is included?

Problem Description Note: I originally posted this question on Stack Overflow but was referred to this community instead. I have a graph containing selectors and elements. An element can have multiple selectors associated with it. As a graph, it…
Akilan Manivannan
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3
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1 answer

Is a subtree of a minimum spanning tree a minimum spanning tree of the subgraph spanned by the subtree?

Let $G$ be a connected weighted undirected graph. Let $T$ be a minimum spanning tree (MST) of $G$. Consider removing an edge $e=(a,b)$ from $T$, which will give two subtrees $T_a$ and $T_b$, where $Ta$ contains the vertex $a$ and $T_b$ contains the…
user119710
2
votes
0 answers

Finding a circle within a circle

Let $G=(V,E)$ be undirected, and let $s,t\in V$ and $C\subseteq E$ be a circle that contains $s$ and $t$. Assuming $s$ and $t$ are on the circle $C$, we are given a set of edges $F\subseteq E$ which are to be removed. After removing these edges, we…
Eric_
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1 answer

Can graphs have a serialized canonical form for the purpose of very fast graph structure look-up (subgraph isomorphism)?

Let suppose we order the nodes first by degree (in + out), to get a list of node structures: Node: labels: [] # lexicographic ordered out_arrows: [] # ordered by ordering of the nodes in_arrows: [] # ordered by ordering of the…
Daniel Donnelly
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1 answer

Find the directed subgraph with least edges that preserves connectivity

I have a directed graph $G$ with a set of nodes $N$ and a set of edges $E$ with the following property : if $(A\to B)\in E$ and $(B\to C)\in E$, then $(A\to C)\in E$, for all nodes $A,B,C$. I would like to find the subgraph $G'$ with the same set of…
Tristan Nemoz
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1 answer

Do graphs with a bounded number of incident edges have a polynomial-time subgraph-isomorphism algorithm?

It is well known that the subgraph isomorphism problem is NP-complete. And so a polynomial-time algorithm for solving it would mean P = NP. Thus I'm interested in whether a bounded version of the problem has a polynomial time algorithm that is…
Daniel Donnelly
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Determine if there's a $P_3$ as an induced subgraph in a graph $G$

Given a graph $G$ on $n$ vertices with $m$ edges, show an algorithm that determines if there's a $P_3$ as an induced subgraph in $G$ in $O(m+n)$ time. ($P_3$ is the path on 3 vertices). What I was thinking at first is that any vertex $v$ that has…
giorgioh
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How to calculate delta Q (modularity increase matrix) in graphs?

I've been trying to implement the Three-stage Algorithm to compare its results with our new proposed algorithm with different datasets than those mentioned in the article. I've succeeded in implementing the first two stages. The third stage,…
Imen Z Imanou
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1 answer

Is CMCG (Constrained Maximum-Weight Connected Graph) problem NP-complete?

MCG Problem: Consider a positive integer R and an undirected graph G = (V, E), in which each vertex is assigned a weight (or value). The maximum-weight connected graph (MCG) problem is to find a subgraph with R vertices that is connected and…
Mamun
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1 answer

Subgraphs of DAG minimizing overlap

Given a DAG, it has a number of 'source' nodes - nodes whose in-degree is zero. Each source node has a set of nodes reachable from it. I would like to partition the source nodes into $k$ disjoint partitions, where $k$ is a fixed parameter, such that…
Ari Fordsham
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Densest Sub Graph and forbidden Pairs

Given two graphs $G$ and $F$ on the same vertex set $V$. Compute a sub set $\tilde{V}\subset V$ which' sub graph of $G$ is of maximum density and does not have any pair that is connected in $F$. Formally, find $$ arg\max_{\tilde{V}\subset…
Daniel Schwegler
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3 answers

Algorithm to find Minimal Spanning Subgraph

I'm attempting to solve this problem: Given an undirected connected graph $G=(V,E)$ with $\mathrm{weight}(e)>0$ for all $e \in E$, and a subset $S \subseteq V$, we define that a sub-graph $H=(V',E')$ of $G$ spans $S$ if $S \subseteq V'$ and $H$ is…
Aishgadol
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Finding highly-connected regions of graphs

I have a large network of 10,000 nodes and I am trying to identify subgraphs which are clique-like, in that they share many connections. I don't a priori know how many subgraphs fit this criteria. To solve this task, I have been trying to use the…
Gabriel
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