Science topics: MathematicsGraphs
Science topic

# Graphs - Science topic

Graph Theory is a branch of combinatorics, here we discuss the theory and application of graphs.
Questions related to Graphs
Distance Sequence!
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A distance sequence of a tree is a non increasing one, consisting of the distances between any two leaves of the tree. Given a distance sequence, can the tree be reconstructed? Common I'm looking forward for your solutions! ;)
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Does anyone know of good texts/books/examples discussing uncertainty in qualitative data visualizations (e.g. the graphical equivalent of significant figures or digits)? As a supervisor/reviewer I see many examples where students/authors present a graphical representation of their rather uncertain data, in the form of singular dots, straight sharp lines etc. There must be appropriate ways of visualizing this uncertainty. A reference to a guidebook or source book would be helpful.
There is a fundamental problem with the"uncertainty" of qualitative data in contrast to measurement uncertainty; the problem was taken up by EU in the socalled MEQUALAN project, see e.g. Accred. Qual. Assur. 8 (2003) 68-77.
Qualitative "uncertainty" is best described by the risks of commtting errors of the 1st and 2nd kind.
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This script will help to get the detailed pie diagrams, for GO analysis.
Our proxy setting is not allowing us to get all these graphs.
I want b2g4pipe.sh script and its property file. It is easily to generate all the graphs in command line option . No need to setting the proxy and all these stuff.
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I am trying to analyze the dynamics of protein interaction networks using power graph analysis. I am unable to critically analyze the obtained graph, hence it will be very helpful if I get any inputs regarding analysis of power graphs.
It was another plugin for old Cytoscape. I worked with power graphs only ones, because I mostly deal with metabolic and gene co-expresson networks and not with protein-protein interactions were it can be really useful. So, I think if You need to work with protein networks, it will be good to study this CyOog. I see a lot of manuals in the Internet. http://opentutorials.cgl.ucsf.edu/images/2/27/PowerGraph_Presentation.pdf
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Throughout literature I found that an Attack Graph is used for network security where it captures all the paths an attacker could use to reach their goals. Here I am looking for new real time application areas where I can use the concept of an attack graph. Any suggestion please.
Attack graphs can be used in non network security environments but it would be in principle more difficult to integrate.
For example it can be used in object recognition from scans such as x-rays where if you have successfully discriminated the object with high accuracy (big if!) you can then run through the attack graph to see if it is a knife, gun,  etc. Then you can provide degree of criticality to recognized objects, match it with profile of person, etc.
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Anybody working Seawater metal analysis using ICPMS with FIAS 400 (C-18 column) in this area send me journals paper including method and graph with data details.
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Nowadays complex network data sets are reaching enormous sizes, so that their analysis challenges algorithms, software and hardware. One possible approach to this is to reduce the amount of data while preserving important information. I'm specifically interested in methods that, given a complex network as input, filter out a significant fraction of the edges while preserving structural properties such as degree distribution, components, clustering coefficients, community structure and centrality. Another term used in this context is "backbone", a subset of important edges that represent the network structure.
There are methods to sparsify/filter/sample edges and preserve a specific property. But are there any methods that aim to preserve a large set of diverse properties?
Let's assume you have a large human network such as cell-phones or Facebook users and your network is > 1M nodes.  This network gives the FALSE impression that anyone  is connected to anyone else, by some path, in the network.  But most FB and cell-phone activity happens in local clusters (those 1 and 2 steps away from you).  So rather than look at 1 large component of 1M nodes it makes more sense to look at the natural clusters of dozens/hundreds of people who really know each other (or at least of each other).  So how do you reduce the large component to hundreds/thousands of real life social circles? A human network of > 1000 nodes usually makes no sense from a sociological perspective -- because most people are strangers in large networks.
1) Often the reason we end up with one very large component is that we have set the bar TOO LOW for what an edge is.  If you have edge strength/frequency to work with, move it up to get rid of the noisey connections while retaining at least "weak ties".
2) Many networks have many satellites/hangers on with a degree of 1... hide all of those (you get one or more 2-cores).  This will start to show the natural emergent clusters in the data.  If you still have one large component you may try a 3-core or 4-core... but no more.
3) Betweenness is normally calculated using all geodesics in a component.  Yet, it can also be calculated using just the shorter geodesics (maxing out at 3 steps).  This efficiently find the spanners between clusters.  There iterative removal will leave you with hundreds of natural social circles.  Keep the high betweenness nodes you removed as a separate network -- as the backbone.
4) Investigate the smaller clusters and the backbone to understand both local behavior and global structure.
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There is dagR package fro graph but commands are not very clear and i couldn't get any good commands for G-computation also, if anybody have, it would be appreciated.
Hi Dharma, This paper (full-text available on researchgate) has an appendix with R code for g-computation: https://www.researchgate.net/publication/50419814_Implementation_of_G-Computation_on_a_Simulated_Data_Set_Demonstration_of_a_Causal_Inference_Technique
The only R package i've used for DAGs is dagR.
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I read many papers exploiting modularity maximization to divide networks in clusters.
Nowhere do I  find a clear explanation of which value of modularity can be accepted as significant in order to conclude that a particular division of a network is well defined. Can anyone give some hints?
Andrea,
in my opinion the answer is no. First of all, consider that modularity has been introduced as a function to be maximized by certain algorithms. Hence, there is no "right" threshold to detect a community; the best modularity value is the largest one. In his seminal papers on modularity, Mark Newman claimed that modularity values above .3--.4 are usually good indicators of community structure. But research on graph modularity has been largely developed since then, and various shortcomings of modularity are nowadays well acknowledged. On the theoretical side, in ResearchGate there is a very nice paper here: https://www.researchgate.net/publication/230996366_Bad_Communities_with_High_Modularity
Another good paper you should read (at least, the first two sections) is this:
In conclusion, I agree with Albert's answer: In community detection, one should not consider modularity alone.
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I am simulating an OTDR in Optisystem and I am using matlab to import the rayleigh scattering formula to Optisystem. When I run the Optisystem, it load the matlab code and the graph is plotted, but there is no output from matlab component on Optisytem though when I go to matlab and display the output it gives a result.
I really didn't get your problem , But regarding my experience ,sometimes it's because of  the Matlab's FUN  analyzer or generally the kind of version you use .
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I have calculated the property (X) for 560 molecules. For some molecules, the values of the X are 0, for some1, for some2 like that and extends up to 10. Now, I want to draw A bar graph with range of the property (0-1, 1-2, 2-3, etc.,) on X-axis and the population (5%, 10%, ...) percentage on Y-axis (as shown in the graph present in the attachments) to find out the range of the property that is present in the maximum % of the population.
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I have real data of various cellular components, and dispersion over time in various stress situations. I want to make an average 3d model per time in each stress using the data. I tried Virtual Cell and other softwares like that, but all are based on simulations and not on real data.
I propose this solution:
- Transform the models in point cloud;
- Regiter all models with respect to a reference (eg CAD model);
- Save the new point cloud;
- By using Matlab, import clouds of points and, for each point, evaluate the average.Regarding the points to consider in the average, this depends on how the models are; they may be the respective points or those closest to each point of the reference model
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In diffuse phase transition the value of Gamma approaches to 2. But in my case I got the value of gamma greater than 2. What can be reason behind it?
Gamma more than 2 can simply mean that you have chosen a wrong maximum for Tm. This is possible if you have two peaks (instead of one) at T=Tm1 and T=Tm2. Let us assume that Tm2>Tm1. For each peak we have related Gamma. Namely,
Gamma1=Ln(1/Er-1/Em1)/Ln(T-Tm1)
and
Gamma2=Ln(1/Er-1/Em2)/Ln(T-Tm2)
where Em1 (Em2) is the maximum value of Er at Tm1 (Tm2).
Most likely (with good accuracy) we can assume that Em2=Em1 (or very close). In this case we get a rather simple approximate relation between the two Gammas:
Gamma2=Gamma1*{Ln(T-Tm1)/Ln(T-Tm2)}
Since for Tm2>Tm1, always Ln(T-Tm2)<Ln(T-Tm1), we immediately obtain that Gamma2>Gamma1. Therefore, even for the largest value of Gamma1 (=2), we  will have Gamma2>2.
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I want to know the work done on connectivity of regular and triangle free graphs.
Thank you for your response. Most of these papers talk about edge connectivity but i want to know about (vertex ) connectivity of k- regular and triangle free graphs.
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The workshop is part of the 2014 IEEE International Conference on Big Data to be held in Washington DC on October 27, 2014.
Program co-chairs: Jiangzhuo Chen, Sandeep Gupta.
Call for papers: Papers for the workshop ‘Big Data in Computational Epidemiology’ at IEEE BigData 2014 should be submitted through the IEEE BigData submission system (http://bit.ly/1oSAkAk). Please refer to IEEE manuscript templates (http://www.ieee.org/conferences_events/conferences/publishing/templates.html) for submission guidelines.
Important dates:
Aug  30, 2014: Due date for full workshop papers submission
Sept 15, 2014: Notification of paper acceptance to authors
Sept 25, 2014: Camera-ready of accepted papers
October 27-30, 2014: Conference
BCDE 2014 -- IEEE Workshop – Big Data in Computational Epidemiology
Computational epidemiology aims to understand the spread of diseases and efficient strategies to mitigate their outbreak. It studies dynamics in socio-technical systems, where disease spread co-evolves with public health interventions as well as individual behavior. It has evolved from ODE models to networked models which apply agent based modeling and simulation methodologies. Computation of such high resolution models involves processing data sets that are massive, disparate, heterogeneous, evolving (at an ever increasing rate), and potentially unstructured and of various quality.
The workshop brings together researchers from epidemiology, data science, computational science, and health IT domains to tap the potential of emerging technologies in data intensive computations and analytical processing to advance the state of art in computational epidemiology. The central theme of how to manage, integrate, analyze, and visualize vast array of datasets has wider applications in the bio- and physical- simulation and informatics based sciences such as immunology, high energy physics, and, medical informatics.
The workshop welcomes original research related to computational models and methodologies developed for handling big data and their application to epidemiology. Topics of interest include:
Collection and generation of large scale epidemiological datasets
Management, provenance, storage, and archival of surveillance, synthetic, and experiment data
Analytics of spatial, temporal, relational, and semi-structured data
Mining social media data and other online data for public health
Simulation driven statistical methods for knowledge discovery and forecasting
Cloud, streaming, and high performance data intensive science
Semantic web tools, informatics, inference, and integration of public health data
Privacy in the big data era
Agent mining, multi-agent systems, agent based modeling, and behavior modeling in epidemiology
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Apart from representing the shortest path length distance among the vertices of the graphs and revealing the connectivity among its vertices, I would like to know if there is any other property that one can obtained from just observing the distance matrix of a given graph.
Hi John and Chis,
Thanks for your response. I am invertigating on distance matrices of simple, connected and undirected graph. Specifically, i am invertigating on its determinant, characteristic polynomials and eigenvalues.
I know for instance the determinant is dependent on the structure of the graph except for trees, complete graphs, complete bipartite graphs and star graphs. In your view, what do you think the determinant of the distance matrix explains about the graph.
For example, does large determinant value implies large path lenghts among the vertices?
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Graph theory and mathematical logic, are both parts of Discrete Mathematics syllabus. Some logical equalities can be express by rooted trees.
Dear Qefsere,
a simple example is a graph model of mathematical logic - vertices are statements and directed arrows correspond to logical implications (a->b if a implies b).
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An updated sample selection is being determined for one of our most comprehensive energy establishment surveys, to more efficient estimate for the current population, as the sample has not been reselected in seven years. There are many combinations of categories for which we report, using small area estimation, and we would like to use some clear graphics to show management comparisons between test results using the past sample and the new one, also including before and after sample sizes, and before and after relative standard errors. I have JMP software on my PC at work, but I primarily just use it for running scatterplots. Does anyone have any suggestions for graphical presentations using JMP that would display the above comparative information well? Thanks.
Try using JMPs Attribute/variability platform.  It is located in the pulldown menu Analyze->Quality/Process->Attribute/Variability/Gauge.
I do not think you need the statistical functions that this will give you, however, if you add your data to Y, and then list the groups you want to show the sampling difference in , then have the last x be a label for which sampling method you used.  This will create a plot that shows for each reported type of data, the difference in the sampling plan.
Another method may be to use the Analyze fit Y by X where the Y's are the data you sampled, and the X is the sampling method.  You can then set up the BY group as a column in your dataset that lists the test type.
Much of using JMP comes down to how you arrange the data going in.  I like to have a column that lists the split, or sample group, a column that lists the tested parameter, and then one for the actual value.  This enables the first type of analysis that I mentioned.  I hope this helps get you started.
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I think both are time and space consuming, there must be something better!
hello,
i believe that the table in the attached file summarize the possible options for graph data structure with complexity;
Regards;
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I have got a model with four indicator variables and four interaction effects. Two of the interaction effects are relevant and significant at least on a 10% alpha level (N = 100).
Do you know a tool or a way to plot these interaction effects in one graph?
Hi there,
I found a solution in stata plotting the indicator scales on the fitted values of the DV (see attached).
What do you two think?
MM
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I have measured gene expression across eight time points, and multiple comparisons show many differences between the time points. I'd like to indicate these significant differences on my bar graph. Usually I would draw a line above the relevant bars and put * or ** above the line, but there are so many differences that the lines would become unwieldy and I feel my graph would just look too messy! Any suggestions? Should I just relegate the p values to a table?
I had a similar problem when looking at the EMG of 8 different muscles and different exercises. I allocated individual symbols to each then added the description under the graph. e.g.,
# Significant difference from 1
† Significant difference from 2
‡ Significant difference from 3
¥ Significant difference from 4
¢ Significant difference from 5
¤ Significant difference from 6
● Significant difference from 7
Ø Significant difference from 8
*Significant difference from all
Then if the result were significant from 1,2 and 3 I added # † ‡ above the relevant bar in the graph etc.
The study I am doing just now has less permutations of significance but still requires tidying up. I have opted for a slightly different approach by doing the following.
* = Significant difference from all (p < 0.05)
*** = Significant difference from all (p < 0.001)
\$ = Significant difference from 1, 2 and 4 (p < 0.05)
¥ = Significant difference from 2 and 3 (p < 0.05)
¢ = Significant difference from 4 (p < 0.05)
Obviously can be altered to your study.
Hope this helps.

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Is blue vs. red and pink dead?
For more information on how to choose colors in your graphs that are friendly to colorblind people: http://jfly.iam.u-tokyo.ac.jp/color/
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My earlier expectation regarding the sufficiency of 4CT to adress this issue, is not correct.
you might also be able to make a counting argument, since k_9 has 36 edges and any decomposition into two parts has at least 18 edges in one or the other part (so you might be able to prove a K_3,3 or K_5 must be in one part or the other)
none of this proves that the 4-color theorem cannot be used, but there are other possibilities
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I have got first peak at 100 C which is the transition temperature from Ferroelectric to paraelectric according to literature. But at higher temperature i got another peak of dielectric maxima. What we can say about that peak. I here attach a graph.
Dear coleague, if th first peak is linked to the transition ferro-para then second anomaly could be related to oxygen vacancies. Heat treatment in controled condition eliminates thispeak
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Need to have access to cells that participate in Selective Boolean. Which kernels (opensource, or free-for-students) give access to the cell graph, inspite of being Brep/feature-based?
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How to fix error bar in Origin 6.0 graph? also how to fix error bar in tabular column?
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I need to determine all odd cycles in random cubic graph. I guess that complexity of this problem for general graph is exponential. Is the situation better for cubic graphs?
if you mean listing them out, then you need exponential time since their number may easily be exponential already for planar graphs:
Consider the triangular grid graph with nodes (i,j) with i = 1, 2, ..., n and j = 1,2, ..., n having (i,j)(i',j') as an edge if and only if:
either the Hamming distance between (i,j) and (i',j') is precisely 1
or j'=j+1, and i'=i+1
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I understand the standard deviation, and how to get to standard errors, but not sure I understand the logic why standard errors could be used.
Sorry, but when i read your question i can interpret it in different ways,
first:  Do you need to know why you have to present either way but you can't present both of them;
Second:  why should you present  either of them in a graph;
or
Third:  Do you need to present something else and excel does't let you to do so?
I can respond to the first and the second, for the third need more information.
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how can we present the statistics clearly ?
Also, if you are not comfortable writing your own code (R is a scripting language), there are several menu driven applications for using R and helping to learn the language. Deducer (http://www.deducer.org/pmwiki/pmwiki.php?n=Main.DeducerManual) and Rcmdr (http://socserv.mcmaster.ca/jfox/Misc/Rcmdr/). As Paulo mentions, SPSS also has a good reputation (I'm not familiar with Prism). It can be expensive to use proprietary software though (like SPSS, SAS, Matlab).  So I usually recommend that if someone is going to learn something new, why not learn how to use Opensource/Free software.
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Seems this should be a FAQ, but I do not have the technical vocabulary for an effective search. I have a large number of observational units (~4000) in ten groups.
using SPSS package for large data or Matrix analysis are used
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Let G=(X U Y,E,P) a weighted bipartite graph, we need to find a matching of maximum cardinality for which the length of the longest edge is minimized.
Compute the max cardinality matching without constraints using your favourite algorithm. Let C be its cardinality.
Then for each k=1,..,|E| remove the k longest edges from the graph and compute the unconstraint max cardinality matching. Return the matching for the largest value of k that has cardinality C.
Speed-up: Use binary search to find k.
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VosViwer is a very poferfull tool in bibliometric analysis but When I select the text corpus option, and then Scopus files I get either a run-time  error message or a very sparse density graph, with just few terms analyzed.
I've never had this kind of problem. Even working with 200,000 documents and selecting titles and abstract.
What version of VOS are you using?
How many RAM has your computer?
Can you send me the Scopus files, or unless part of it, to test it?
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In a k-connected graph  an edge is contractible if contraction of the edge yields a k-connected graph.
I am not entirely sure if this is what you are looking for, but this paper may assist (from my understanding of the Graph Theory you are discussing).
Contractible Edges and Triangles in k-Connected Graphs by Ken-ichi Kawarabayashi, Journal of Combinatorial Theory, Series B (2002).
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Currently I am measuring the binding of FITC labelled peptide to a protein using fluorescence polarization technique. However, even in the absence of peptide (buffer alone) I am getting higher fluorescence polarization value. Moreover, when I measured the fluoresce polarization of my FITC labelled peptide alone at various concentration from 100nM to 10uM, I am getting decreased fluorescence polarization upon increasing concentration of peptide. I wonder why buffer alone (131mP) or peptide at low concentrations (133mP) giving higher fluorescence polarization compared to peptide at higher concentration (10uM-31mP)
I am using Perkin Elmer 96-well plate reader (serial number-431460). Excitation wave length 485nm and emission 530nm and pH of buffer is 8.
I also attached the graph of FITC peptide fluorescence polarization at various concentrations.
Can anyone explain why buffer alone or peptide at low concentrations gives higher polarization?
Thank you.
Likely you a dividing noise by noise. Measure spectra at the polarizations separately at polarizer orientations VV, VH, HV and HH using the dwell time you specified and examine the curves individually. In order to carry out an anisotropy/polarization measurement accurately you need sufficient counts in the VV and VH curves. You also need the HV and HH curves in order to carry out a grating factor which is the bias for one orientation with respect to the other.
Time-Resolved fluorescence anisotropy can be more useful. I made a tutorial video on anisotropy of FITC, FITC-Trypsin and FITC-BSA yesterday:
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I want to fix error bar in graph and tabular column in my paper. Please give the details how to fix it.
Which paper?
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I have multiple excel files (~100) in a folder. Each time I have to process it to plot graph in matlab. Is there any coding to process all graph and plot it?
You can use the xlsread command to open data from an excel file.  I have attached a basic example of how you might use it to generate plots from all the excel files in a directory.  Save the .m file to the directory you want to process, hit 'F5' to run it, and then approve the change in directory, and it should generate a plot for every .xlsx file in the folder.  It can be easily modified to work for .xls files as well, notes are given in the file.  The data can easily be processed once it is loaded, just insert processing commands before the plotting statement.
Best of luck!
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Is the graph that you found  connected
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I want to know the basic details of error bar in graph and tables.
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I've been trying to compare my results to another study and I need these peaks d-spacing values in order to determine the average d-spacing to make the comparison but I'm not sure how to identify them. If anyone could give me any tips I would be most grateful, thank you!
If you are asking how to identify the peaks then.... The easiest way is to compare your results with standard databases (JCPDS etc).  These database give you theta or 2theta (i.e. angle) values for each crystal planes of your material.
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EQE: external quantum efficiency
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I have problem with Rössler attractor. I do not know how to create bifurcation diagrams. I have tried to solve differencial equations by Runge Kutta 4, but my bifurcation diagrams are still wrong despite that graph of Rössler attractor is correct. Please, could you advice me how to establish bif. diagram correctly. I do something wrong but I do not know what.
Dear Lenka!
Sincerely yours Vasiliy Belozyorov
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I have a graph generated from Globplot which I cannot understand. The only thing I can understand is that there is a continuous stretch of disordered region from approximately residue number 800.
Thank you
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I'm obtaining poor values in higher paper. On the same conditions with a BCR of 160 I'm obtaining CMT=350N and with a BCR=190 CMT=190N. And the graphs are completely different. I am very confused.
Thank you very much.
I have found an answer. If you use starch on the surface instead of in the pulp, CMT test will have two peaks. The problem is where you put on the starch
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I got the scheme graph as attached. Can I determine the molecular weight of the polymer? I don't understand whether the data is correct or not.
Iam not sure these signals true or not. These signals seems to be noise. I was also find these type of signals  with sample or without sample also. Since absolute intensity very less ,signals also very week. In MALDI-MS signal intensity 3 times higher than noise. I think you can try with ferulic acid as a matrix.  It can work for high molecular weight compound. Further more polymer spectrum never look like these. We will get signals like tree with continuous. See the attachment paper may help you.
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Dear all,
I would like to plot radial density curve for my spherical lipid system. I have plotted RDF graph using gromacs utility g_rdf as shown below:
gmx rdf -f traj.xtc -s topol.tpr -n index.ndx -o rdf.xvg -cn rdf_cn.xvg -bin 0.05 -com
How to post-process the output (rdf.xvg or rdf_cn.xvg) to get radial density plot (1/nm^3 vs nm)?
Thank you.
If that means that you have a function Y=1/x3 as a theoretical hypothesis, then you may plot the mathematical values of Y vs X for x>0. And if you have datasets with variables X,Y, you may study this third function Y=1/x3 from real data, measure its media, and make other analysis to compare empirical results with the theoretical ons. Is it the purpose of your research?
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How to display results in graph, plot or hyperplane of svm with w ,b and svs etc.
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I am looking for a compact encoding of directed graphs, in particular regarding the linear (without pointers) encoding, suitable for streaming.
There are a few algorithms out there for chemical applications that convert molecular graphs into line representations. One output format is called the SMILES format. http://pubs.acs.org/doi/abs/10.1021/ci00062a008
you could use the same concept to convert your graph into a single word. If the number of of nodes in your graph is n, then the number of characters in your "SMILES" word is also n
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I know the vertex set of total graph T(G) is the union of V(G) and E (G). Two vertices x,y in the vertex set of T(G) are adjacent in T(G) if any one of the following holds
(i). x,y are in V(G) and x is adjacent to y in G
(ii). x,y are in E(G) and x,y are incident in G
Your definition of the total graph is incomplete. The vertex set of T(G) is the union of V(G) and E(G). The edges are as follows:
(i) If u and v are vertices which are adjacent in G, then uv is an edge of T(G),
(ii) If e and f are edges of G which share an endpoint in G, then ef is an edge of T(G),
(iii) If u is a vertex of G and e is an edge of G such that u is an endpoint of e, then ue is an edge of T(G).
Alternatively, T(G) is the "square" of the graph obtained by subdividing every edge of G. For more information about total graphs and squares of graphs, see the links below.
Solution needed within 2 days
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Given an undirected graph G=(V,E) where V=V1 U V2 U V3 and E is a subset of { {u,v} | u is in V2 and v is in (V1UV3) } Now the problem is to determine a set X which is a subset of V2 such that TP+TN become maximum where: TP= | {v : v is in V1 and there exists a vertex u in X such that uv is in E } | TN= | {v : v is in V3 and there is no vertex u in X such that uv is in E } | .
:) That's great but I don't think the person who asked me this still need that! LOL!
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What are the sufficient conditions to be satisfied by a graph for, it is not Hamiltonian?
Rakesh, would you like to continue P vs NP discussions here? http://www.researchgate.net/topic/P_versus_NP_problem/ . The problem of finding the Hamiltonian cycle definitely falls there.
A sufficient condition is:
- For a vertex v1 there exist vertices v2, v3 and v4 such that
1) every path from v2 to v3 goes through v1 (i.e. there is no path from v2 to v3 without visiting v1), AND
2) every path from v3 to v4 goes through v1 (i.e. --"-- v3 to v4 --"-- ), AND
3) every path from v4 to v2 goes through v1 (i.e. --"-- v4 to v2 --"-- )
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Is there any software to various types on named graphs and to study about their properties?
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The concept of semi graph is new. So I am working on this topic.
I am also working on this topic. I am also search the current reaseach in semi graph.
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On the CPAN, we find Graph 0.94 (by Hietaniemi), but it only gives betweenness centrality (and false results for diameter). There is also BoostGraph (only shortest paths).
Does anyone know Perl modules to compile clustering coefficient and any modularity or graph segmentation algorithm ? How would it be possible to use within Perl the Gephi modules (written and freely available in Java) ? Is there something like Jython in Perl ?
Sure yes
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In frequency assignment, it is very important to find a lower bound of minimum span of frequency assignment problem. Up to 2007 the lower bound are known but after that I don't know whether this bound was improved or not?
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In its 0.8.1, the Gephi software provides a community detection algorithm with a tunable "resolution". It is a great tool that enables changing the focus of the detection of communities. Give a smaller or bigger resolution, and you have more or less classes.
But there is no bibliographic reference to explain where this resolution comes from. Unless I have not noticed it, the Blondel et al. (2008) paper does not provide any resolution tuning. Does anyone have have first-hand sources about this tuning ?
You have likely found the answer already, but for others who are interested, the resolution factor comes from R. Lambiotte, J.-C. Delvenne, M. Barahona, Laplacian Dynamics and Multiscale Modular Structure in Networks, 2009.
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It can be advocated that a graph is a powerful representation for several kinds of systems. Does anyone use them to study self-organizations? It think it has been argued that the study of the degree power law of a graph could give clues for the evolution of the system.
Any further idea?
See book of A.N. Sharkovsky, V. Fedorenko et. al. Of course, the graph theory can be applied to the one-dimensional dynamical systems. For example, for unimodal maps.
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I use the "Louvain" algorithm (Blondel et al., 2008) in Gephi to detect communities in graphs. This algorithm provides a modularity value Q as sort a "quality-control". The higher the value is, the best the result should be.
Gephi (versions < 0.7) said that it Q < 0.4, the result should not be considered too seriously. Is this an absolute answer? Are partitions with Q < 0.4 really bad results? Uninterpretable results? Nonsense results?
I also used the Louvain method quite often because its so fast. But there are two things to say about modularity. First a value smaller than 0.4 is not automatically bad. Because if you for example calculate it on the Zachary's karate club dataset (can be found at the page of Newman) using the original partition gives a modularity of 0.36 (or similar i don't remember it correctly), however the original partition is not the "most" modular. A second thing is the resolution limit of modularity. A nice description is given here: http://www.pnas.org/content/104/1/36.abstract.
Therefore the question what modularity tells you in general is not really solved.
In general, modularity is a nice metric but not the best in all cases. This is to my knowlege what most people would tell you (and told me).
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Watts, Strogatz (1998) tell that their clustering coefficient denotes sort of a "cliquishness". Does it refer to homogeneity of a subpart of a graph? I'm working on lexical text graphs (a node represents a word, an edge represents co-occurrence of two words) and would be interessed to learn interpretations of this metric.
When you ask for an interpretation does it mean that you want an NLP interpretation of your coefficient? If yes, the closest your lexical graph is to a clique (cf previous explanations on the local clustering coefficient), the more your text focuses on a single semantic field, according to your graph building method. If you get a clique, or a quasi-clique, it means that all your text words tend to be highly co-occurrent. This seem to happen to words describing a given semantic field, or a conventional script.
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Ulam's conjecture:
Let graph G have p points v_i and graph H have p points u_i, where p>=3. Then if for each i, the subgraphs G_i=G-v_i and H_i=H-u_i are isomorphic, then the graphs G and H are isomorphic.
It is difficult to prove because the sequences in which corresponding vertices are removed from both graphs usually does not coincide, but finding 'the correct' pair of interchangeable vertices to remove at a definite time is a problem on its own.
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What are the current topics of research interest in the field of Graph Theory?
Graph Labeling is one of the major research areas on which so many research is going on at present.
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How could one give vertex magic total labeling to a tree?
Can u define magic vertex labelling?
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Open Research Topic • Riffs & Rotes
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Open Research Topic • Logical Graphs
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I recently found out that there is a link between planar graphs and distributive lattices, e.g. certain sets of orientations of a planar graph form distributive lattices. When i read a theorem stating that a lattice is distributive if and only if it has no sublattice isomorphic to N5 (the pentagon lattice) and M3 (the diamond lattice) it struck me that there is a huge apparent similarity to the planarity argument in graphs where a graph is planar (on S0) if and only if it doesn't not contain a subdivision of the graphs K5 (the complete graph with 5 vertices) and B3,3 (the complete bipartite graph with 2 partitions with 3 vertices each).
Since my actual work is in a different field i cannot spare the time to really investigate this on my own, yet i am very interested in a possible connection here. So does anyone here know of a paper/thesis or similar that expounds on or disproves this apparent similarity?
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Give me detail about supersubdivision of graphs
Dear Researcher,
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Is there any applications of magic labeling in other fields?
Kavitha what is your progress now in magic labeling
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Given an arbitrary graph, Is there any method to construct a bipartite graph which represents the given graph faithfully.
We are looking for a function B, which generates for each graph G a bipartite graph B(G) with the
properties :
For two graphs G and H the bipartite graphs B(G) and B(H) are isomorphic if and only if G and H are isomorphic.
Such a function B is not difficult to find:
Starting with a graph G with vertex-set V and edge-set E we construct B by putting a new vertex in every edge of G. The new graph B(G) is bipartite, because old vertices are only connected with new vertices and vice versa. The graph B(G) has |V|+|E| vertices and 2*|E| edges.
The proof of the properties above is an easy exercise.
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hey all wonderful people here,
can we discuss different efficient algorithms for matching of two graphs....
warm regards,
Chetan
Here is a polynomial-time - O(N^5) - algorithm for that: http://www.researchgate.net/profile/Sarge_Rogatch/blog/45524_Fix2_polynomial-time_algorithm_solving_Graph_Isomorphism_problem . It is correct almost everywhere. If you find someone who pays for this work, I will provide further details and make the last few steps.
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There is a very nice description in terms of semi-rings in Alex Vardy chapter on trellises in The Handbook of Coding Theory...
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Can we find algorithm used in facebook friends location Graph? It wonderfully creates a graph according to friends locations
It google map based utility. Wri
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Any procedure for vertex and edge labelling of a graph
Hey Senthil,
Welcome to the group!
and
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Vertex coloring in which no two neighbors of the same vertex are having same color
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List colorings was defined by Vizing/1976, Erdos et al./1979.
Each vertex is a radio tower with a list of frequencies = colors. Two vertices are adjacent if they cannot work at the same frequency  at the same time.  The minimum number of colors (=frequencies) is the list chromatic number.
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I thought bar graphs with different colors for each group, but Excel nor STATA include this option.
Would you elaborate a little more on what you'd like to do, and what those groups are?
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I'm implementing the algorithm in the context of grammatical dependency graph pattern matching. The "simple enumeration algorithm" is fine but I'm not familiar enough with matrices to understand why condition (1) works. What is M(MB)^T = C, semantically?
Thanks
MB tells us which adjacencies the vertex selections in M should have. M(MB)^T works out which of these it actually has. This can then be compared with the adjacencies described in A to check if it is a match.
To extend this to work for directed graphs, we must either transpose it again [i.e. C = (M(MB)^T)^T] or swap the indices in the comparison, [i.e. (a_{i,j} = 1) => (c_{j,i} = 1)]
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Does anybody have a good book or articles, an introductory one, on the Pythagorean graphs?
If you take the definition like in http://www.ijser.org/paper/A-Note-on-Cordial-Edge-Cordial-Labeling-of-Pythagoras-Tree-Fractal-Graphs.html then the dual is easy to characterize as the dual of a tree which is the universal cover of (3,4) bipartite biregular graphs. It is also easy to generalize to universal covers of (k,l) graphs.
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When plugging in errors for a simple bar chart of mean values, what are the statistical rules for which error to report? I guess the correct statistical test will render this irrelevant, but it would still be good to know what to present in graphs.
Very good advices above, but it leaves the essence of the question untouched. The CI is absolutly preferrable to the SE, but, however, both have the same basic meaing: the SE is just a 63%-CI. The SD, in contrast, has a different meaning. I suppose the question is about which "meaning" should be presented.
The SD is a property of the variable. It gives an impression of the range in which the values scatter (dispersion of the data). When this is important then show the SD.
THE SE/CI is a property of the estimation (for instance the mean). The (frequentistic) interpretation is that the given proportion of such intervals will include the "true" parameter value (for instance the mean). Only 5% of 95%-CIs will not include the "true" values. If you want to show the precision of the estimation then show the CI.
However, there is still a point to consider: Often, the estimates, for instance the group means, are actually not of particulat interest. Rather the differences between these means are the main subject of the investigation. Such differences (effects) are also estimates and they have their own SEs and CIs. Thus, showing the SEs or CIs of the groups indicates a measure of precision that is not relevant to the research question. The important thing to be shown here would be the differences/effects with their corresponding CIs. But this is very rarely done, unfortunately.
Can any body help me in finding out what are the current trends in Random Graphs?
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I want to read and work in Random Graphs.
You need to read the basics first, like http://www.iecn.u-nancy.fr/~chassain/djvu/SpencerStFlour.pdf and then proceed on. There is a lot of info about random graphs online, like http://www.youtube.com/watch?v=kXfca4CqSo0 and much much more! Good luck!
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We define state space and map input in state space and output as a combination of the state variable. If we define a transfer function with two variables s1 and s2, then how can we define the minimal state space form for this transfer function?
For example, if T(s1,s2)=(s1+s2)/s1s2-1, and the minimal state space has an imaginary value in minimal state space, what is the meaning of imaginary in this realization? And how can we migrate from complex variables to real, and import a real state space from this realization?
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The only pertinent reason I am able to identify is for presentation purposes. That is, sometimes data points cluster at the really low end of the concentration axis, making it very difficult to see what is happening. But where that is not the case, is there any other reason that compels me to log my concentrations?
Peter -
Usually when a log is taken, it is to make a nonlinear relationship look approximately linear. It can also be part of dealing with heteroscedasticity. However, although this is popular, I think it is not often advisable, as it can distort your perception of the problem being addressed.
My guess is that in your field, a log transformation will make this dose response curve appear linear, when it isn't, and as you said, it could spread out those points so they could be better seen. However, be careful how you interpret the slope of such a 'linear' regression. As you suggested, this seems like a less than optimal approach, but I suppose it has some advantages. An alternative that comes to mind would require two graphs: You could do one graph without taking a log, and show a second graph that is just a 'blow-up' of the problem area. You could then investigate some nonlinear regression options.
A book that I found interesting, that you might also enjoy is as follows:
Carroll, R.J., and Ruppert, D. (1988), Transformation and Weighting in Regression, Chapman &Hall. (I think it may have been reprinted by CRC Press.)
Cheers - Jim
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I want to delete a given number M of vertexes (with adjacent edges) of a given graph G with N vertexes to split the remaining graph G' into minimal number of independent sets. Or, alternatively, to color it with a min number of colors. Graphs are sparse and huge, M is much less then N.
Thanks, Vitaly, this is what we are thinking to do as well. At least it is fast enough. Nlog(N) or so on N edges ?
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I am working on circular layout, I need a mechanism to pass vertices of a graph in some particular order (for edge crossovers minimization) to circle graph layout. But there is no parameter in circle graph layout definition which accepts the vertex ordering.
Is there any way I could do that? Or how shall I change the vertex sequence of a boost graph so that circle graph layout will automatically plot the vertices in desired sequence ?
I am working on clustered graph using boost subgraph.
I've got no experience with the boost library, but why not
arranging the layout by yourself? You have to find a
permutation such that intersections are minimized. No vector
arithmetic is necessary since in this special case there is
an easy characterization. If you walk around the circle,
beginning at a node with an edge, ending at its graph
neighbor, all edges of vertices between must have both
ends in the set of vertices you will encounter on the walk.
You have to minimize the sum of violations. Seems
like a kind of Travelling Salesman problem, but with only
few nodes Threshold Accepting or Simulated Annealing
should suffice.
Regards,
Joachim
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How to draw editable figures and graphs?
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I have tried to search this topic over internet, however, I can't get a very clear picture about bi-partitioning. Understanding that bi-partitioning is splitting a graph into 2 partition, my concern is that the do the partition have to be symmetric in term of size, weight, and so on?
You split (divide, partition) the vertex set into two parts=subsets in such a way that no edge connects two vertices from the same part. If you have a hypergraph (collection of subsets=hyperedges of a given set), then bi-partition means dividing of the vertex set into two parts in such a way that no part contains any of the subsets=hyperedges of the hypergraph.
Question
Could someone assist me on how to display a graph in python?
I have downloaded and installed the canopy enthought environment for my python code.
However, when I use the plot command from pylab, it does not display the graph even though no error is generated. I am quite new to python. Kindly tell me how to display the graph.
Below is the sample code:
import numpy
import pylab
pylab.interactive(True)
y=numpy.array([2,3,4,5,6,6])
print y
x=pylab.linspace(-1, 1, 20)
pylab.plot(x, x**2, 'o-')
is missing at the end to display the graph.
Have a look at the following link giving you a very general workable plot program
or with tinyurl
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...
The number of non-isomorphic trees is also known as a sequence A000055: http://oeis.org/A000055 . You may see references in that article and the formula for the generating function there. According to Wikipedia ( http://en.wikipedia.org/wiki/Tree_%28graph_theory%29 ), there is no known closed form formula for the number of unlabeled non-isomorphic trees.
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For a given integer n, how to determine the smallest size of graphs satisfying the Ore-condition? i.e., finding the minimum graphs that satisfy the sum of the degrees of any non-adjacent vertices being at least n.
If I understand your question right, the minimum such graph is simply a triangle - trivially so, as there are no pairs of non-adjacent vertices.
The smallest non-trivial example would be a square. There are two pairs of non-adjacent vertices, each with total sum of degrees being n = 4.
Grappa Libraray
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How to setup with grappa java libarary? http://www2.research.att.com/~john/Grappa/
What is the application of irregular labelling or total vertex irregular labelling?
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My project is about total vertex irregularity strength, and some of my friends ask about it's application.
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.
sudo apt-get install python-setuptools
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I face the task of laying out a weighted graph that will change the number of nodes during runtime. The chosen layout should rearrange the nodes without losing the global topology in order to keep the "amount of visual adjustment" as low as possible for the user. Additional requirement: it should be applicable in a JAVA-environment. Does anyone know the best practices?
I'm also coming from Java world and at some point used DOT+Graphviz. However, recently I found JavaScript libraries rendering to either html5 canvas or SVG easier to use. I would look into sigma.js (http://sigmajs.org/) or d3 (d3js.org). Especially the latter offers a great level of customization. One of the good thing about Gephi is that it offers force-based layouting algorithms, and sigma.js has its own implementation of Gephi's Force Atlas2 algorithm.
How can we draw median graphs with a diameter of 8?
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Is there any way to draw median graphs of diameter 8?
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Is there a well defined structure to keep graphs in memory?
The usual ways of representing graphs is either with adjacency matrices
or with with lists of nodes (structs, records, objects) that themselves
contains lists of pointers to their neighbors (or indexes of neighbor nodes).
Recently there was a publication about GraphChi,
an algorithm where most of the graph is
stored on harddisk when RAM is too small.
Another trick is the Bloom filter. It's a probabilistic way of
compressing a graph.
If you use it for example for storing edges, false edges
are possible, but not false non-edges. An application
might be reachability. When a node can't be reached
via the edges encoded in a Bloom filter, then it's
sure that it can't be reached in the original graph.
Regards,
Joachim
Question
I'm looking for all the techniques used to prove hamiltonicity
to Christian Moewes, thank you for your answer but i'm not interested by the algorithmic aspect or the complexity of the problem, i know that it is NP-complete, in fact I am looking for the techniques which are used to prove that a graph with some specific properties is Hamiltonian, for example there is the "hopping lemma" and its variants and i want to know if there is another "classical" techniques.
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I am creating a project which "transforms the C code" to flow graph. Please suggest any tool or any materials. Should I change the compiler intermediate code to any specification of graph transformation system?
Thank you Alexandre Chapoutot...
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Csv file consists of x, y, z (three colums). I have to load those three colums values into matrix & then i have to plot x vs y, x vs z.
x y z
1 11 13
2 8 45
3 13 18
4 85 106
To load data from a CSV (assuming it contains no errors):
dim datafile as string
dim dataarray(1000,3) as single ' rows, columns of an array
dim cc as single
datafile = "c:\......." ' the filename - or get it from an object
FileOpen(1, datafile, OpenMode.Input)
Do while not EOF(1)
input (1, x)
input (1, y)
input (1, z)
cc=cc+1
dataarray(cc,1) = x
dataarray(cc,2) = y
dataarray(cc,3) = z
Loop
The other things - plotting - good luck
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