Code covered by the BSD License

### Highlights from grTheory - Graph Theory Toolbox

4.54286
4.5 | 35 ratings Rate this file 113 Downloads (last 30 days) File Size: 34.3 KB File ID: #4266 Version: 1.3

# grTheory - Graph Theory Toolbox

### Sergii Iglin (view profile)

16 Dec 2003 (Updated )

28 functions for different tasks of graph theory

File Information
Description

GrTheory - Graph Theory Toolbox.
Functions:
grBase - find all bases of digraph;
grCoBase - find all contrabases of digraph;
grCoCycleBasis - find all independent cut-sets for a connected graph;
grColEdge - solve the color problem for graph edges;
grColVer - solve the color problem for graph vertexes;
grComp - find all components of graph;
grCycleBasis - find all independent cycles for a connected graph;
grDecOrd - solve the problem about decomposition of the digraph to the sections with mutually accessed vertexes (strongly connected components);
grDistances - find the distances between any vertexes of graph;
grEccentricity - find the (weighted) eccentricity of all vertexes, radius, diameter, center vertexes and the periphery vertexes;
grIsEulerian - find the Eulerian cycle of graph;
grIsomorph - solve the problem about isomorphism for two graphs;
grMaxComSu - solve the maximal complete sugraph problem for the graph;
grMaxFlows - solve the maximal flow problem for the digraph;
grMaxMatch - solve the maximal matching problem for the graph;
grMaxStabSet - solve the maximal stable set problem for the graph;
grMinAbsEdgeSet - solve the minimal absorbant set problem for the graph edges;
grMinAbsVerSet - solve the minimal absorbant set problem for the graph vertexes;
grMinCutSet - solve the minimal cut-set problem for the digraph;
grMinEdgeCover - solve the minimal edge cover problem for the graph;
grMinSpanTree - solve the minimal spanning tree problem for the graph;
grMinVerCover - solve the minimal vertex cover problem for the graph;
grPERT - solve the project evaluation research task;
grPlot - draw the plot of the graph (digraph);
grShortPath - solve the shortest path problem for the digraph;
grShortVerPath - for digraph with weighted vertexes solve the problem about the path with minimal weight of verticies;
grTranClos - built the transitive closure for the digraph;
grTravSale - solve the nonsymmetrical traveling salesman problem;
grValidation - auxiliary function (the data validation);
grTheoryTest - test program for all functions.

Required Products Optimization Toolbox
MATLAB release MATLAB 7.0.1 (R14SP1)
Other requirements PC
26 Apr 2016 Han Li

### Han Li (view profile)

I'm trying to use grIsmorph, but is asking for function psimilar...
Where can I find this?

Comment only
27 Mar 2016 V L

### V L (view profile)

03 Mar 2016 komal

### komal (view profile)

kindly give detail about how to install n use grtheory tool box. given information is not complete. help me please

Comment only
17 Oct 2015 abishek ganesan

### abishek ganesan (view profile)

i have installed this grtheory toolbox
Can anyone tel me how to work with it please

good gooop

23 Mar 2015 sam esa

### sam esa (view profile)

dear sir, I would ask if matlab toolbox function have function or program on Binary Decision Diagram algorithm ... thank you

16 Oct 2014 Chenjie

### Chenjie (view profile)

20 Aug 2014 Liang

### Liang (view profile)

24 May 2014 Muhammad Abrar Akber

### Muhammad Abrar Akber (view profile)

MIQP is missing to use grTravSale, How and where to get it?

Comment only
10 Oct 2013 Rohini Sharma

### Rohini Sharma (view profile)

please tell me how to rin this in MATLAB.

Thanks

Comment only
31 Jul 2012 Yonggon

### Yonggon (view profile)

Sumantra, make sure your graph is connected. As long as your graph is connected, you should get correct result.

For this one, with arbitrary edges to make the graph connected without introducing any new cycle, I get
2-5-7-2, 2-5-8-11-7-2, and 2-5-8-14-15-11-7-2.

Comment only
26 Jul 2012 Sumantra Sarkar

### Sumantra Sarkar (view profile)

I think there is a bug in the grCycleBasis function. I have a large edge matrix, a part of which is:
2 5
2 7
5 8
5 7
7 11
8 11
8 14
11 15
14 15

Clearly, there are three cycles in this graph. viz. 2-5-7-2, 5-7-11-8-5 and 8-11-15-14-8. However, the function fails to recognize these three cycles individually and returns 2-5-8-7-11-2 and 2-5-8-14-15-11-7-2, completely ignoring the edges 5-7 and {5-7,8-11} respectively. It happens for several other subsets also. Please suggest a solution.
Thank you.
p.s. It calculates the number of cycles correctly though.

Comment only
12 Mar 2012 Martin

18 Jan 2012 kira

### kira (view profile)

Hi:
I'm also trying to use grIsmorph, but is asking for function psimilar...
Where can you find this?

Comment only
18 Nov 2011 Nina

### Nina (view profile)

Hi! I am trying to run grTheoryTest for isomorphism (case 12) but it's looking for the function or method psimilar. I googled for the file psimilar.m as well as search this site for it. Help? Please? Pretty please, I need this to work in a week :(
Also, do you know how to do subgraphs? Apart from doing a for while removing and adding various vertices?

Comment only
28 Mar 2011 kira

### kira (view profile)

Hi, I have a question using grplot...
For my purposes, I need to draw digraphs with 'vplotstyle'='ko'... and I also need that the arrows don't go to the center of the nodes, ie, not to the vertex position, but to the edge of the circles... I'm looking at the code, and I have identified the vector that generates the edges... but I still don't know how to modify them to do what I want... Could you give some clue...
Greetings...

Comment only
02 Oct 2010 Tianfan XUE

### Tianfan XUE (view profile)

Excellent Job! Thank you very much!

30 Jun 2010 Sergii Iglin

### Sergii Iglin (view profile)

The size of task is determined by the function BINTPROG.

Comment only
09 Jun 2010 Wang

### Wang (view profile)

There is something wrong with grMinVerCover.m and grMinEdgeCover.m when worked in large-scale complex networks(1000 nodes, 2500 edges). The result are both empty cell matrix. But it works well in small-scale networks.
So I want to konw whether there is limited to input data.
Thank you.

19 Apr 2010 Sergii Iglin

### Sergii Iglin (view profile)

>> E=[1 2;1 4;1 5;2 3;2 4;2 5;3 4;3 5;4 5]
E =
1 2
1 4
1 5
2 3
2 4
2 5
3 4
3 5
4 5
>> nMS=grMaxComSu(E)
nMS =
1
2
4
5

Comment only
30 Mar 2010 Tomaz

### Tomaz (view profile)

I think there is even more serious bug in grMaxComSu.m than Florian suggested.
For example, I forwarded the function following set:
E=[1 2;1 4;1 5;2 3;2 4;2 5;3 4;3 5;4 5]
function returned completely wrong result.

If I don't seriously misunderstand concept of max complete subgraph, the solution should be graph with nodes 1,2,4,5.
However, function suggests non-logical solution: 1,2.
Can somebody please re-test this and confirms the problem or explain to me, where does my logic go wrong?
If somebody already encountered this problem, I would appreciate if she/he would share with us the observation or even a solution.
Sergeii great overall work and it would be really nice to see this bug removed...
Does anybody know any other public file for solving the problem of searching max complete subgraph?

Comment only
02 Sep 2009 Florian

### Florian (view profile)

does exactly what I'm looking for!
A minor bug in grMaxComSu.m

If the graph itself is a clique e.g. [1 2; 1 3; 2 3] the function gives an error. E1 in the code is then empty. Possibly account for this cas in a future version. Great work!

19 Nov 2008 Andrew Jackson

### Andrew Jackson (view profile)

11 Sep 2008 Chao Wang

good job

26 Aug 2008 rose rose

very good!

19 Aug 2008 li pengfei
18 Aug 2008 Tim Davis

Comment to Swamy Korada: Finding all possible paths between 2 nodes is an NP-hard problem. Any such algorithm would either give an approximate solution, or take exponential time.

Comment only
10 Aug 2008 fan fanwen

Great work

Is there a script to find all possible paths between 2 nodes?

Comment only
07 May 2008 Andi Patombongi
06 May 2008 jason tharmaraj

can you send me complex networks analysis codes

Good package it sounds!
One additional question: Could the input be thousands of nodes in one graph?

19 Oct 2007 xue huiyan

thanks

19 Oct 2007 hiro mano
28 Sep 2007 gloria macapagal

it is very good toolbox

28 Jun 2007 li yifan china
22 Jul 2006 wael rashwan
20 Oct 2005 giu giu

There are some bugs

31 Aug 2005 Pablo Riera

Excellent

25 May 2005 sanith Wijesinghe
10 Apr 2005 Igor Yegorkin

Beautiful job!

02 Apr 2005 Vlastislav Weiner

Salesman problem doesn't work without miqp function. But where could I find it???

Comment only
29 Dec 2004 Zhenya Donchik

I`m very interesting by the theory of managment

13 Dec 2004 Alexandre Felt

Great job, works fine!

14 Jun 2004 Michael Waisberg

The plotgraph function only works well with small graphs. It produces awful graphs when using more than four vertex. The toolbox could come with some function to format the data. I used one called cedge.m which worked well. Also, to use this toolbox you will need to install at least arrow.m.

12 Mar 2004 ahmed kolsi
23 Feb 2004 Nick Valuy
12 Feb 2004 Alex Pesch

I think, the Optimization Toolbox is required. The function MaxFlows for example is not running here, because 'linprog' doesn't exist.

Comment only
21 Dec 2003 x s

A bug in grPlot is corrected.

24 Dec 2003

Draws the graph and solves the tasks: Maximal Flow, Maximal Matching, Minimal Vertex Cover, Minimal Spanning Tree, Shortest Path etc.

20 Jan 2004

Draws the graph and solves the tasks: Maximal Flow, Maximal Matching, Minimal Vertex Cover, Minimal Spanning Tree, Shortest Path etc.

09 Feb 2004

ShortPath had update for fast calculation

26 Aug 2004

14 Sep 2004

PlotGraph is updated

11 Oct 2004

CycleBasis is updated

28 Mar 2006

All functions are updated, new functions are added.

30 Mar 2006

Summary title is updated

26 Apr 2006

The function grMinAbsEdgeSet are included.

09 May 2006

two new functions are created.

16 May 2006

29 Jun 2006

Two new functions is added. One function with bugs is deleted.

05 Jul 2006

08 Aug 2006

The function grDecOrd has update.

11 Jul 2009 1.1