# Questions tagged [subgraphs]

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### Fully Connected Graph to Lattice

I am looking for algorithms (or at least something similar to the problem definition): Given a fully-connected weighted graph $G$ with $n$ nodes, find a subset $S$ of edges that form a square lattice ...
59 views

### Is a predecessor subgraph always connected?

Given an undirected graph $G$ with non-negative edge weights, how can we prove that the predecessor subgraph $G_{p}$ of $G$ is always connected? Here's how the predecessor subgraph is defined: for a ...
1 vote
38 views

### 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 $F$. ...
37 views

### 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 $v\in V_2$ ...
15 views

370 views

### Subgraph Isomorphism Problem NP complete?

I found many solution online on how to reduce Subgraph Isomorphism problem to Clique, but how do I prove that it is NP complete by reduction from independent set? I'm struggling to figure out this ...
41 views

### 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 ...
1 vote
46 views

### 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 ...
215 views

### 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 ...
1 vote
66 views

### 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: ...
117 views

### 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 ...
58 views

### 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 ...
387 views

### 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 ...
265 views

### 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 ...
108 views

### Find subgraphs that can only be reached by two nodes

I want to find subgraphs in a graph that are only connected to the rest of the graph by two nodes; for example, node A is connected to the rest of the graph, as well as node F, but nodes B-E are only ...
119 views

### 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 ...
61 views

### 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 ...
Consider an undirected graph $G = [V,E]$. Let $V$ be the set of vertices: $V = \{v_1,..,v_n\}$ and $E$ be the set of edges. Let $C$ be the connected component that contains vertex $v_1$. I want to ...
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 $Ta$... 