Questions about properties of and problems on graphs, discrete data structures that have the form of nodes connected by edges, that is networks.

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undirected graph without weights and DFS

following question on undirected graph without weights can be solved by using DFS and in O(|V|+|E|) times. check that G is ...
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1answer
53 views

Finding a Hamiltonian Path through the complete graph on 37 vertices: $K_{37}$

I'm planning on making a fiber art $K_{37}$ (like the one I laser etched with help: K37: The complete graph on 37 nodes, svg). To accomplish this, the plan is to construct 37 pegs equally spaced in a ...
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0answers
16 views

Is it possible to find closeness centrality using Gephi? [on hold]

I'm a newbie to Gephi. I need to calculate the centrality measures. Is there an option/plugin available to calculate them ?
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45 views

Equivalent Straight Line Embedding of a Planar Graph Drawing on a Grid

Two embeddings of a planar graph in the plane are called equivalent if one can be continuously deformed into the other. I am looking for a reference which shows that any Jordan arc embedding of a ...
4
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1answer
40 views

Parameters for Barabasi-Albert graph generator

I'm trying to reproduce the synthetic networks (graphs) described in some papers. It is stated that the Barabasi-Albert model was used to create "scale-free networks with power-law degree ...
4
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0answers
77 views

What is this prize-collecting optimization problem with travel times?

There exist very rich literature on discrete optimization problems such as variants of knapsack problem, traveling salesman problem, orienteering problem, tourist trip design problem and etc. ...
2
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1answer
24 views

Examples for directed graphs with super polynomial cover time

The cover time of a graph is the expected number of steps in a random walk on the graph until we visit all the nodes. For undirected graphs the cover time is upperbounded by $O(n^3)$. What about ...
-1
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0answers
16 views

Distance Increment in Graphs [closed]

Question: Let G be a direced graph with non-negetive weights and to speciall nodes S and T,find the smallest group N (group of edges) that will increase the distance form S to T. Time ...
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1answer
32 views

Not Hamiltonian is in NP Class? [duplicate]

I ask a question before, Questions on Graph and Hamiltonian, but i ask it here with different challenging contest. From this book and other study in complexity theory, I have seen the following ...
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3answers
93 views

How can I evaluate an algorithm for a NP-Hard problem?

I have written a program to calculate the number of stable partition in a graph. ( That is: find which partition of the nodes does not have edges between nodes of the same block. ) The professor, ...
2
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1answer
70 views

Questions on Graph and Hamiltonian [closed]

From this book and other study in complexity theory, I have seen the following statement: The definition of NP is not symmetric with respect to yes-instances and no-instances. For example, it is ...
4
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0answers
25 views

Parallel algorithm to find if a set of nodes is on an elememtry cycle in a directed/undirected graph

I'm looking to find / develop a simple parallel algorithm that does this: Input: vs: list of root vertices max_length: max cycle length max_dist: max distance to root Variants one variant of ...
2
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1answer
32 views

What is an edge hop?

I've tried googling it, but found nothing. Here is the context it's in: From Bayesian Reasoning and Machine Learning: Adjacency matrices may seem wasteful since many of the entries are zero. ...
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1answer
56 views

“Minimum” maximum flow with extra capacities

Problem: Suppose there is a graph, a source and a sink. Each edge has a capacity and an extra capacity that it can hold. If sink needs a defined amount of flow F, ...
2
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1answer
72 views

Disconnecting a complete graph by removing edges randomly

Given a complete graph with $n$ nodes, I remove edges randomly with probability $p$ such that I want to disconnect the graph. I want to find out the minimum number of edges that I must remove ...
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0answers
61 views

Clique vs genus [migrated]

Is there a relation between Clique size $\omega(G)$ and genus $g(G)$ of a graph? That is does $$\omega(G)^c\geq g(G)\geq \omega(G)^{\frac{1}d}$$ hold with constants $c,d\geq1$?
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1answer
63 views

Union grouping in bipartite graphs?

I'm trying to figure out a good (and fast) solution to the following problem: I have two roles I'm working with, let's call them players and teams having many-to-many relationship (a player can be on ...
2
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0answers
19 views

Heuristic for weighted maximum independent set in graph with ~$2 \times 10^5$ nodes and $|E| \propto |V|$

I want to find a near-optimal solution for a maximum weight independent set. i.e given a graph $G = (V,E)$ I want to find a set $S = \{v_1,v_2,\dots,v_n\}$ of nodes in $V$ such that the sum of their ...
4
votes
1answer
79 views

Term for a matching which is perfect on one side only

What is a standard term for a matching in a bipartite graph, in which one part has less vertices than the other part, and the part with less vertices is fully matched (but the other part is, ...
6
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1answer
404 views

Why is the complexity of negative-cycle-cancelling $O(V²AUW)$?

We want to solve a minimal-cost-flow problem with a generic negative-cycle cancelling algorithm. That is, we start with a random valid flow, and then we do not pick any "good" negative cycles such as ...
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0answers
10 views

Solving $Isomorphism$ using $AUTOM$ in polynomial time

Let $Iso$ be the language of all $<G,H>$ such that $G$ and $H$ are isomorphic, and $AUTOM$ be the language of all $G$'s such that $G$ has a non-trivial automorphism. I'd like to show that, ...
0
votes
2answers
31 views

A* graph search heuristicfor pathfinding

A* needs a consistent heuristic to work on a graph. So I'm not sure if the heuristic of a straight line (bird flight) can be used. For example: the costs to travel to a neighbors node is always ...
2
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0answers
41 views

Constructing orthogonal latin square Parker/Knuth method

I'm working through Knuth; The Art of Computer Programming, Vol. 4 Fascicle 0 and I'm having a little trouble making sense of the method Knuth describes for computing an orthogonal latin square. The ...
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1answer
22 views

Reweight general weighted graph to distinct graph for using Borůvka's

Is it possible to re-weight a generally-weighted graph to a distinctly-weighted graph to apply Borůvka's algorithm (wiki) for minimum spanning tree to it? I can't seem to think of a way to make a ...
8
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1answer
477 views

Does a graph always have a minimum spanning tree that is binary?

I have a graph and I need to find a minimum spanning tree to a given graph. What is to be done so that the output obtained is a binary tree?
2
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1answer
54 views

Reduction from a further constrained problem

If I find an NP Hard problem that is equivalent to my problem with an additional constraint or bound, can I still prove that my problem is NP Hard? Generally, this is probably not the case. For ...
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3answers
226 views

number of edges in a graph

I got a problem related to graph theory - Consider an undirected graph ܩ where self-loops are not allowed. The vertex set of G is {(i,j):1<=i,j <=12}. There is an edge between (a, b) and (c, ...
3
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1answer
82 views

Linear programming formulation of cheapest k-edge path between two nodes

Given a directed graph $G = (V,E)$ with positive edge weights, find the minimum cost path between $s$ and $t$ that traverses exactly $k$ edges. Here is my attempt using a flow network: \begin{align} ...
5
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3answers
294 views

Constructing a random Hamiltonian Cycle (Secret Santa)

I was programming a little Secret Santa tool for my extended family's gift exchange. We had a few constraints: No recipients within the immediate family Nobody should get who they got last year The ...
5
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1answer
72 views

Finding $k$ claws ($K_{1,3}$ bipartite graphs) in a graph?

Usually questions deal with claw-free graphs, but suppose we are given a graph $G$ and there are $k$ vertex-disjoing claws in the graph, how can we derive a randomised algorithm using color coding to ...
0
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1answer
194 views

Proving that the cover time for graph is exponential in the worst case

How can I prove that the cover time for a directed graph $G$ can be exponential in the size of $G$? The cover time is the expected length of a random walk that visits all vertices.
2
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0answers
54 views

What is a best known algorithm for finding diameter of undirected graph?

What is best known algorithm (approximate or exact) for finding diameter of a large undirected graph? The diameter is defined as longest of shortest paths between any two nodes. I know that naive ...
4
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0answers
56 views

Recognize if graph has Hamiltonian cycle from subgraphs

There is a graph G, which is not known to me. Instead I am given the multiset of all graphs that are obtained by deleting a single vertex from G. My task is to figure out, from all of these subgraphs, ...
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3answers
81 views

Given a minimum vertex cover can we find all the others in polynomial time?

Having found one minimum vertex cover of a connected undirected graph, is there a known polynomial-time algorithm for finding all the other minimum vertex covers of the graph, or is this problem ...
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1answer
58 views

Finding undirected cycles in linear time (triangulating graphs while minimizing degree)

In the article ["Triangulating Planar Graphs While Minimizing the Maximum Degree"] by Kant and Bodlaender [1], Section 4 briefly mentions the extraction of elementary cycles (no repeating ...
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0answers
54 views

Maximum flow problem with non-zero lower bound

Given $G = (V,E )$ a directed graph, if $ X \subseteq V $ we write $$\begin{align*} \delta ^{+}(X) &= \{ xy\in E \mid x \in X, y\in V - X \} \\ \delta ^{-}(X) &= \delta ...
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1answer
33 views

To detect isomorphic graphs Is it enough to check if they have the same number of same degree vertices?

Given two lists of non directional graph edges e.g. [(1,3),(3,5),(5,1),(5,7)] [(4,5),(2,3),(3,4),(4,2)] In order to check if the two graphs are isomorphic is it enough to count the vertices with the ...
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0answers
18 views

Algorithm: “Minimum” maximum flow with extra capacities [duplicate]

Problem: Suppose there is a graph, a source and a sink. Each edge has a capacity and an extra capacity that it can hold. If sink needs a defined amount of flow F, ...
1
vote
1answer
62 views

Knight's tour from all starting positions

Is it true that for all $n\geq 5$, there is a knight's tour of an $n\times n$ chessboard beginning at every square? For example, is it correct, that there is no solution for a $5\times5$ board, with ...
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35 views

Stable Marriage or Assignment Problem?

I have a question pertaining to committee selection. Let $C = c_{1}, c_{2}, \ldots, c_{n}$ be n Committees and $S = s_{1}, s_{2}, \ldots, s_{m}$ be m Students. Each $c_{i}$ in C ranks their ...
3
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1answer
21 views

Do $s$-$t$ cuts partition contingent vertices?

The definition of an $s$-$t$ cut is a partition of the set of vertices $V$ into $2$ sets $(A, B)$ with $s$ in $A$ and $t$ in $B$. My understanding of set partitions is that the positioning of elements ...
3
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0answers
73 views

Steiner tree wiring problem

I’m trying to find an algorithm that can give me an approximate solution for a wiring problem that I have been asked to look at. I believe this is closely related to finding a node weighted Steiner ...
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0answers
63 views

Need an upper bound for node degree

I have a social network in the form of an undirected graph $G = (V,E)$ with distinct non-negative integer keys. For each node $u \in V$, let the set $\Gamma(u) = \{ v \in V : (u,v) \in E \}$ be the ...
0
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1answer
42 views

Tournament graph

I have to prove the following assertion: given a tournament graph with $n$ vertices, $n\geq 5$, there can be made an arrangement of the arcs such that between any two vertices exists at least one way ...
0
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0answers
13 views

Graph Partition Across Cluster - Minimize Largest Matrix Size

I am writing some code for modeling semi-biologically realistic neural networks, which is to be run/distributed across nodes in a computer cluster. I begin with a very large adjacency matrix ...
9
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1answer
111 views

Determining the minimum number of edges to add in order to be 3-connected

A graph $G$ is said to be $3$-connected if it has no $2$-vertex cutsets (i.e., at least three vertices must be deleted to disconnect the graph). As far as I know, it is possible to determine if a ...
13
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0answers
109 views

Finding an st-path in a planar graph which is adjacent to the fewest number of faces

I am curious whether the following problems has been studied before, but wasn't able to find any papers about it: Given a planar graph G, and two vertices s and t, find an st-path $P$ which minimizes ...
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2answers
43 views

Can't see how this can be true: any connected undirected graph $G$ contains vertex v such that removing v results in another connected Graph $G'$ [closed]

I am attempting to prove this result but I found a case where I can easily disprove this statement. Suppose $G$ is a graph with two nodes u, v and an edge (u,v) and respective self edges, then ...
4
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1answer
51 views

Distribution of cycles length in a graph

Given a random directed Graph G: $$ G=(V,E) \\ \lvert V \rvert = n , \lvert E \rvert = k $$ where for each vertex, either: $$ d_{incoming}(v) = 1 , d_{outgoing}(v) = 1 $$ meaning - for each ...
2
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0answers
43 views

Necessary and sufficient condition for unique minimum spanning tree

This is an exercise problem (Ex.3) from the excellent lecture note by Jeff Erickson Lecture 20: Minimum Spanning Trees [Fa’13] . Prove that an edge-weighted graph $G$ has a unique minimum ...