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The R function centralityPlot plots by default variables in alphabetical order, but I am considering to sort them according to their domain. 
I already used the label option assigning abbreviations (i.e. NC1, NC2, SC1, SC2,...) and got the variables belonging to the same domain close to each other, but in this way the single constructs are not immediately recognizable. So a user-defined sorting would solve my problem, is it possible?
thanks a lot
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This is a late reply, but I'm posting it in case other researchers are still looking for an answer.
Currently, in centralityPlot of qgraph, the default value of the "orderBy=" option is set to alphabetical order. This is because 'gtools::mixedsort' is used internally. If you modify this part with the rev() function, you can check that the nodes are displayed in original order from the top. If you want the reverse, you don't need to use rev().
original source:
L55:
nodeLevels <- unique(gtools::mixedsort(as.character(Long$node), decreasing = decreasing))
If you want to plot the centrality graph:
1. in order from the top
nodeLevels <- unique(rev(as.character(Long$node)))
2. in order from the bottom
nodeLevels <- unique((as.character(Long$node))
Hope this helps. :)
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I have microbial networks for more than 2 groups(6). I want to analysis the community structure and network properties among these networks all at the same time. Any web based or R-based tools would be helpful to me. Additionally I am also looking forward for tools that can be used to analyze the longitudinal nature of microbiome data and provide the networks or other attributes of microbiome. Any help and suggestions are welcome. Thanks
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Talking about network comparison, you can opt for different topological comparisons network the groups.
R has lots of packages for that.
Cytoscape is also an option.
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I would like to design a microgrid based on an IEEE bus system for the purpose of validation of a certain technique. Should the MG have the same standard loads of the IEEE bus system ?
Can I design the MG (say based on 14 bus system) and have only few Kilowatts as a load (50 KW load) , does this make sense or it deems impractical?
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A system has to be evolved based on the generation and load requirements. If we try to use lower loading in the system designed for higher capacity there will be a under utilization of the system capacity.
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Can someone explain me what are the common layer 3 problems that happen in a network? specially in SOHO environment if possible.
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I preprocessed resting state fMRI by GRETNA toolbox to do graph theory analysis. After preprocessing step completion, when I saw the normalization quality check for data I found the following problem (see attached figure).  I checked to compare the EPI image before pre-processing and figure after normalization, before and after figures are the same cut from above. So I thought that problem is not related to normalization or other steps of the preprocessing. Am I right? I am new to this area. I want to know the reason for this error and should I exclude this subject from my network analysis?
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As you described that before and after pre-processing the images looks same, this asserts that normalization didn't do anything. Dataset look fine to and I think there is no need to exclude from analysis.
Suggestion; 1) make sure it happen to only this subject? 2) if yes, read its header file to find difference from other subjects.
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Hi, RG community! I am new to network analysis and I am currently facing a challenge with coding, processing, and quantifying networks in a hierarchical scheme. In this scheme, nodes pertain to differing hierarchical ranks and ranks denote inclusion relationships. So, for example if node “A” includes node “Z”, it is said that “A” is “Z”’s parent and “Z” is “A”’ daughter. However, a rather uncommon feature is that nodes at different ranks of the hierarchy can relate in a non-inclusive fashion. For example, node “A” parent of “Z” may have a directional link to “Y”, which is “B”’s daughter (if “A” were directionally linked to “B”, then it could be said that “A” is “Y”’ aunt). Here is a more concrete example to illustrate the plausibility of this scheme: “A” is a website in which person “Z” is signed in (inclusiveness; specifically, parentship); website “A” can advertise banners of website “B” (siblingship) or recommend to follow a link to person “Y” profile in website “B” (auntship).
OK. So, in the image below (left top panel) I present a graphical depiction of this rationale. For simplicity, a two-rank hierarchy is used, where gray and red colors denote higher and lower hierarchies, respectively. The image displays siblingship, parentship, and auntship links. My first approach to coding this network scheme was to denote inclusiveness as one-directional relationships (green numbers) and simple links as symmetrical (two-way; brown numbers) relationships (see table in right panel). However, I soon realized that this does not reflect what I expected in networks’ metrics. For example, I am mainly interested in quantifying cohesiveness and the way I coded the network in left top panel entails something like the non-hierarchical network depicted at the left bottom panel. In short, I am not interested in the directionality of the links but in actual inclusiveness. To my mind, the network in the top panel is more cohesive than that in the bottom panel but my coding approach does not allow me to distinguish between them formally.
The solution conceived in the interest of solving this problem was to stipulate that a relationship between any pair of nodes implicates a relationship of each with all of the other’s descendance. This certainly yields, for example, the top network being more cohesive than that in the bottom, which is in line with my goals. However, this solution is not at all as elegant as I would have hoped. Can anyone tell if there is a better solution? Maybe another way to code or an R package allowing for qualitatively distinct relationships (not just one-way or two-way). Thank you.
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Instead of listing A/B on the same level (in matrix) as Y etc, what you say you want seems (to me) a graph G = [X,Y,Z,W] with 2 subgraphs A, B.
A simple representation then is a matrix 4x4 and a datastructure to test if a node is in a subgraph or not (dictionary/set).
If you want to model edges between A/B, you can define a new 2x2 matrix describing those.
Note that for large datasets adjacency matrices will scale poorly, so either a adjacency list or sparse matrices can be useful.
There is a fast datastructure for this kind of problem (if A/B are disjoint)
If you find you need multiple edges, consider hyper/multigraphs
Hope this helps,
Ben
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I have Scopus data of articles. I want to do a citation network analysis s to detect the structure of the community of citation networks in the past literature. I have seen many tutorials. But could not do it in Gephi software. Can someone help me do it in Gephi or any other software?
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1. Use bibexcel to create a .net file;
2. import .net file in Gephi to build network graph
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Hello to all,
I have previously performed gene expression analysis using R to find hub genes that were significantly different in expression from control genes, I mean differentially expressed genes (DEGs). In some articles I red about weighted correlation network analysis (WGCNA) that its concepts is very similar to those of finding DEGS.
I want to know if anyone has ever done WGCNA in R?
Does it have a special command?
Do I have to install a specific DEGs package? Or Is this analysis different from the gene expression analysis that determines the DEGs ?
I am very grateful for the guidance of experts in this field.
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Dear Shafagat Mahmudova Thank you so much.
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Hello
I want to camparing two Psychiatric groups in their connections .
But, because of our financial limitation , we need the minimum sample size.
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The sample size always depends on the reference population.
Also, you need to clearly set the goals of the analysis.
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The problem of self-interaction effects and errors arises in studies of, for example, anions, electrons, atoms and molecules.
It also arises in developing a theory of network effects in connection with network entropy (for example, https://arxiv.org/abs/0803.1443 ). In the network case, the concept of degrees of freedom leads to an apparent resolution.
Does the network case generalize?
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you can consult this book
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Hi guys, I am looking for someone who understands the R language and is willing to be a partner in the production of a scientific paper. More specifically in creating a thematic mapping, multiple correspondence analysis (MCA), the k-means clustering, and network analysis of historical citations.
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Luis Alberto Bertolucci Paes, Yes, we can collaborate..
Just for my understanding, I wanted to know Why R?, Why not Python?
To get an idea about the dataset, it would be great if you can share some details about the same through email (shiv@dbit.in).. then we can take if further..
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Hello everyone!
I am currently dealing with some transcriptomic data and building protein-protein interaction (PPI) networks. After filtering my data by fold-change and p-value, I got quite a lot disconnected nodes in my PPI network. So I would like to expand my current network through a whole-genome network (as a template) in order to connect the maximum number of single nodes. The main assumption is that not all proteins being at play in a biologic response will show a change in their transcript level, and that up-regulated proteins may interact with partners (yet present, and unmodified during the biological response). My goal, thus, is to connect the maximum amount of query nodes with the minimum amount of newly added nodes.
The STRING database has an option of "adding more nodes to the current network", but it usually enriches current clusters rather than connecting single nodes (or at least it seems to me). However I don't know what strategy does STRING follow to choose nodes to be added. So, what would be the best network expansion strategy to connect single nodes?
Thanks in advanced!
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Your problem sounds more like a maximum-connected subgraph problem: You can give a positive weight to each query node (depending on how important it is to connect it), and -1 weights to all other nodes. The maximum-weight connected subgraph problem is to find a connected subgraph of maximum node-weight. There is some quite efficient software for this problem. E.g.: https://scipjack.zib.de/
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I'm reading a study which contains the following quotation:
"in many cases there may be limits to the number of relations that any one point in the network can sustain (Scott, 1991: 77). Where this is the case, the actual number of lines possible in any graph will be limited by the number of points in the graph and therefore, all other things being equal, larger graphs will have lower densities".
Can anyone provide me with a further reference or two to back up the idea that larger networks have lower densities?
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The network density is defined as the number of actual connections divided by the number of possible connections. So, if the numerator is constant, network density goes to zero with growing size. An example of a limit for neighbor count is the Dunbar number.
ResearchGate limits the number of people I can follow to 5000, so if I want to follow a new person I've got to choose and unfollow another one.
Regards,
Joachim
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Hello everyone,
I am searching for a road network dataset and its corresponded traffic data. I have found some road network dataset in the web, however, no traffic data has been attached to it. Therefore, I would be grateful if anyone could help me in finding such data.
Thank you in advance.
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Dear Mr. Alizade!
I searched for YOU resources I believe will help you in your work:
1) Droj, G.; Droj, L.; Badea, A.-C. GIS-Based Survey over the Public Transport Strategy: An Instrument for Economic and Sustainable Urban Traffic Planning. ISPRS Int. J. Geo-Inf. 2022, 11, 16. https://doi.org/10.3390/ijgi11010016 Open access: https://www.mdpi.com/2220-9964/11/1/16
2) TIBCO offers quality solutions:
Elise Lakey 2021. Powering the Road to Smart Cities, May 11, 2021, © 2022 TIBCO Software Inc. Free access: https://www.tibco.com/blog/2021/05/11/powering-the-road-to-smart-cities/
Yours sincerely, Bulcsu Szekely
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Dear colleagues,
I am looking for software for Systems mapping and Causal loop diagrams. It would be wonderful if any of you with experience in this could share some information.
Have you used any? Any advice or feedback? Pros and cons?
Thanks in advance,
Fabio
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You can look at these pages.
The focus in more on computation than just representation, though.
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I am new to Organizational Network Analysis and my lecturer told me to seek for a software that does ONA, whether the software is free of charge or not it does not matter. Thank you in advance.
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Hi everyone! I'm working on a network analysis project and have some questions about how to calculate and interpret eigenvector centralization in signed network. Hoping someone can help me out.
Considering a signed network with symmetric adjacency matrix like this:
0 -0.5 0.85
-0.5 0 -0.43
0.85 -0.43 0
and its eigenvector centralities of each node are {0.63, -0.48, 0.61}
Here are my questions:
1. How can I calculate the eigenvector centralization of such network using Freeman's method (with the maximum centrality comparing to every centralities; Freeman, 1978)? I found most papers use this method only in unsigned network.
2. How to interpret the centralization I calculated? I have tried to use standard deviation and gini coeffienct to calculate the eigenvector centralization. But I realized that is problematic. For example, even change the sign of centrality above to {-0.63, 0.48, -0.61}, I will still receive the same centralization. In other words, I can't differentiate whether the network is positively or negatively influenced in general.
I'll be more than grateful if anyone could give me some instructions to my question!
Best regards!
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Let x be eigenvector of the largest eigenvalue λ of the non-negative adjacency matrix A of the undirected graph G = (V, E).
The eigenvector centrality of node i is equal to the leading eigenvector xi of (column) stochastic matrix N := AD−1 (whose leading eigenvalue is 1): Nx = x
Consider a particular node i with its neighboring nodes N(i): xi = ∑ j∈N(i) xj = ∑ j Aijxj
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Hello. I am trying to run a haplotype analysis in PopArt. It's going well until I realized I can not load a previous work in PopArt. I can only export the graphical output as .svg, .png, or .pdf but not as a "network" file which I can reload or edit if I want to in the future. I noticed that it can be saved as a .nex file and the new file actually had additional lines (the portion of the code started with: "Begin NETWORK"). I think this is supposed to be read by PopArt but it fails to do so. I encounter parsing errors when I try to run the new file. I am not sure if there is a way around this as I am new to the software. Any help would be appreciated. Stay safe, anon!
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Great question, thanks for asking.
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I simulated a protein structure for 50ns, I conducted residue interaction energy analysis on the equilibrated last 1ns of the trajectory. Using gRINN, I calculated the pairwise interaction energy of each residue. Now I wish to find out clusters in the protein structure and calculate their total interaction energy ( for each cluster).
Any suggestion will be appreciated. Thanks in advance
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I have a research-related question to how can I easily read my results off a Co-occurrence network from VOS Viewer. Please provide any links to articles I can relate to.
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Dear Dhvani H Kuntawala,
Related to your query, I suggest you follow https://www.youtube.com/watch?v=sW893WYvQGM
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Hi,
I am looking for some article/book/clip about performing and interpreting Network Analysis using R in psychology studies. I would be grateful if you could help me in this matter.
Thank you
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See resources from Sacha Epskamp (http://sachaepskamp.com/) and Eiko Fried (https://eiko-fried.com/).
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I am trying to construct a haplotype network with over 400 mitogenomes with each one of length 15 kbp. I get the notification of "inferring the network" which disappears in a minute and after that the plot area is still blank with no network drawn whatsoever. There is no way to know whether the POPART is still calculating/drawing the network or is just stuck.
Anyone else with same problem? is there any solution?
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Hi Kuldeep More ... Well, I believe it is far beyond the software's capacity, but you might workaround this by first, reducing your dataset for haplotypes only (not all samples), then variable sites only (conserved sites doesn't mater here). Given the size of your dataset, I recommend you to do that with some processing language like Perl, R, Python, or even in bash (in a fasta/vcf aligned file). If you are not familiar with, you might try regular softwares as DNAsp (v6 or higher), MEGA and others. You can still entering haplotypes' frequencies and locality data with "trait blocks/files" (see PopArt manual for details).
DNAsp seems an interesting choice because authors have optimized it to work with SNP data, so it should have the capacity to handle your data (but look at the manual first). Also, DNAsp has a specific module to generate haplotype files for network softwares, exporting data in nexus and other output formats, and generating haplotype frequencies files.
Good luck.
Cheers
Wilson
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I want to find the resonance and anti-resonance frequencies of an ultrasonic transducer by analyzing its impedance.
so I need to buy a impedance analyzer or spectrum analyzer or something like that.
but my budget is limited.
do you recommend any device for my application and limited budget? :D
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If you want to measure impedance in a low cost way, get yourself
1) Suitable signal generator
2) An appropriately sized current sense transformer
3) a two-channel oscilloscope.
Measure the voltage and current as you vary frequency. Oscilloscope will give you the phase relationship between current and voltage across transducer. You can then calculate the real and imaginary components of impedance. I leave it as an exercise how you might calibrate this setup. Cheers!
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Hello everyone! For my dissertation I am using Network Analysis to model my data. I have 11 variables and all but 3 of them are likert scales. I am struggling to test for linearity for my data (linearity is an assumption for network analysis). Obviously when I am trying to test linearity using standardised regressions (ZRED against ZRESID) the scatterplot is not homoscedastic because of the likert scales. Is anyone familiar with Network analysis assumption testing regarding likert-type data??? any help appreciated :) My data is not normally distributed however I am using npn transformations (in JASP) to solve this issue for the networks. Just don't know how to test for linearity as relations among variables need to be assumed to be linear.
I am using SPSS for data cleaning etc. and JASP to run the network.
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From my basic understanding of likert scale analysis, it might be difficult to establish linearity of the constructs of likert scales unless they are transformed to continuous state.
Since you are using SPSS for data cleaning, I believe you can transform the likert scale responses by computation of each item measured on likert scales to generate a continuous variable for each of the item which can then be used to explore the test of linearity.
For instance if the 3 variables are measured on a 4-point likert scale coded as "0, 1,2 and 3" in an ascending or descending order of the score attached to the construct it measured, it means that you will have a maximum reference scale of 3×3 (9) and following computation, the continuous value generated out of a total score of 9 can be used for testing linear relationship, correlation/regression as long as the outcome variable is also in a continuous state, it can also be dichotomously categorized based on the mean score from the reference scale. However, since i can't tell if the items of the variables are measuring the samething or not, I wouldn't be able to conclude whether what can help is transformation by computation or transformation by recoding.
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Dear experts and colleagues,
Hello, all! I recently received a reviewer's comment stating that the proposed network measures of graph theoretical analyses could be correlated by mathematical definition.
So I ran the correlational analyses and global efficiency, characteristic path length, mean clustering coefficient (global measures) showed correlated to each other.
I understand that Global efficiency is inversely related to characteristic path length, but I am quite confused about how characteristic path length is inversely correlated with mean clustering coefficient, while mean clustering coefficient is positively correlated with global efficiency.
Or does my data is wrongly suggested?
Briefly explaining my study, it is a neurological study using MR images (diffusion tensor imaging) to explore the structural networks.
Any feedback and discussion are welcomed here!
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Dear Yae Ji Kim ,
Look the link, maybe useful.
Regards,
Shafagat
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For my doctoral research, I have a dataset of 8 teams, with 2 teams each from 4 organizations, and I am checking peer centrality in team advice networks using centrality. These are directed networks. I have created adjacency matrices and each matrix has 12 to 30 nodes.
Please advice:
  1. Should I test each team network individually or club them to get organizational correlations? Should be there any other partition applied?
  2. What should be my main considerations when working with visualization of small networks?
3.I used the Yi-Fan Hu layout (output) for betweenness centrality related to general workplace advice when I ran the first trials. What should I be using for best rendering?
4. What tests should I run and should I report it in writing?
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hi.,
Kindly Check this link:
Best wishes..
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hello,
im trying to build an IoT dataset for attack detection for my master thesis , the dataset should contain normal and anomaly data,
im using Wireshark to capture the network packets and CICflowmeter to extract the features from the pcap file and generate the CSV, now my problem is how to label each instance of this dataset, is there any script, program, algorithm or equations i could use to label each instance as normal or as udp flood attack .....
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We have to design and use a classification algorithm such as SVM to classify data as normal or abnormal.
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The similarity here refers to the similarity between two networks instead of two nodes in the same network. Node sets of the two networks are not completely different nor same. Besides, the two networks are un-directed, weighed network. How can I measure the similarity between these two networks, any algorithms or tools? 
It seems there are some biological tools to compare certain biological networks. My networks are not biological. However, if a biological tool could measure the similarity between non-biological networks, please let me know.
Thank you.
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The answer to this question is not easy, and it depends on which questions want to answer and which properties of networks are influenced in your research question. One problem is nonlocality. Sometimes even two links are different, some properties of networks will be changed. Please see the following papers:
- Comparing methods for comparing networks, https://www.nature.com/articles/s41598-019-53708-y
- Nonlocal failures in complex supply networks by single link additions, Eur. Phys. J. B 86, 377 (2013)
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I am trying to come up with a code in R to perform network and dynamic network DEA. I would really appreciate if someone knows any available R package that can help me out.
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This package claims it does.
From description: Implements various decision support tools related to the Econometrics & Technometrics. Subroutines include correlation reliability test, Mahalanobis distance measure for outlier detection, combinatorial search (all possible subset regression), non-parametric efficiency analysis measures: DDF (directional distance function), DEA (data envelopment analysis), HDF (hyperbolic distance function), SBM (slack-based measure), and SF (shortage function), benchmarking, Malmquist productivity analysis, risk analysis, technology adoption model, new product target setting, network DEA, dynamic DEA, intertemporal budgeting, etc.
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I want to model the interlinkages between several dimensions using
network analysis. I never used this technique but I just read about it in the relevant literature.
I found Gephi software which seems to be user-friendly but my question is how can I model panel data using the software ( my model include variables such as GDP). is it suitable for such analysis?
many thanks,
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Hi Tara
Here is the thing about networks. You have to define the nodes and edges (links) based on your own interest. If you want to accommodate more variables, then they have to either be as nodes or even as properties of nodes or edges. Once you define this, you can always use a tool like Gephi to perform network analysis. In addition, I would suggest trying your hands around programming languages such as R for efficient and flexible analysis. I don't know if it would help but below are some of the links you can explore. Thanks
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I have a directed graph that ends at point "L". When I sum all the incoming degrees at point "L", I got the value: 13. But I want to modify the graph based on the given plot (see the attached figure). In the graph, the incoming degree will be distributed in the following nodes. For instance, the incoming degree of point "F" is 2 therefore the value for "F" is 2. But in the case of point "K" and "G", the value will be 0.5 and 0.5 because the value of "H" is distributed into two parts. The value of point "J" will be the sum of the incoming values in the upper nodes (i.e., G, E, F).
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Thank you very much .. Tommaso Mazza
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When I study about inductors I found that inductors have a constant value and value of inductance depends upon the permeability of core. And when I see the hysteresis curve then found that permeability depends on magnetising current and initial state of core(if it has retained some magnetism earlier). So I think inductor is non-linear in pure sense but approximated to linear. And in capacitors also due to analogous nature we can predict that it also nonlinear and capacitance is also not fixed due to variable permittivity.
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Dear Sarvesh Singh sir,
Ist part : Permittivity and permeability can be a complex quantity in different mediums if we go further into details. For example, in homogeneous medium, they are constant while for isotropic medium they are scalar constant.
2nd part : Capacitors and inductors can be linear or non-linear which depends upon many factors. Ex- using iron core will show a non-linear behaviour for inductor whereas using air-core will show linear behaviour for inductor. Linearity of these elements also depends upon various factors like medium, material used in the fabrication etc
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The article, Simoiu, C., Sumanth, C., Mysore, A., & Goel, S. (2019). Studying the "Wisdom of Crowds" at Scale. Proceedings of the AAAI Conference on Human Computation and Crowdsourcing, 7(1), 171-179. Retrieved from https://ojs.aaai.org/index.php/HCOMP/article/view/5271 notes that it is (p. 172):
“... one of the most comprehensive studies of the wisdom -of -crowds effect to date ..”
Are there any other comparable studies? If so, can you please provide the citations?
A different approach is to use emergent collectively solved problem sets, such as the English lexicon or rates measuring increases in efficiency for emergent collectively solved problem sets, such as :
1) The rate of improvement in domestic lighting: Nordhaus, W. D. (1994). Do real-output and real-wage measures capture reality? The history of lighting suggests not. Technical Report 1078, Cowles Foundation for Research in Economics, Yale University;
2) The rate of increase in average IQs. A theory of intelligence.arXiv:0909.0173v8;
3) By assuming a general collective problem solving rate, and finding a formula connecting the collective rate with the average individual rate of problem solving:
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This article might be useful, have a look
Kind Regards
Qamar Ul Islam
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I have a question about "network score" of IPA Network analysis. In many papers, the top 5 networks were listed in tables, while in these tables some network scores are high (around 50), but others are low (less than 20). We use the same method for network analyses, and got the impression that we can see tight association between genes when "the network score" is higher than 40. However, we have not found literature discussing the meaningful "network score" (we found one paper described that “the networks are selected if their score is higher than 21”). We would appreciate it if you could let us know information about such a meaningful network score or your impression/experience of the network score (for example, did you see tight association of genes when the network score was less than 20?).
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Anyone have the actual citation for these? They are dead links all of them!!
Kind Regards
R,
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I have 50 survey responses coded as 0 and 1 in a square matrix format pasted on different excel worksheets. I want measure the frequency on 0 and 1 in each cell to identify if 0 is having frequency or 1. What is probable method for it??
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Use the =Countif function to count the number of times each unique entry appears in the original list.
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Can someone provide me with the R code for Network Analysis where I can establish the relationships among the variables using the underlying concepts of SNA using the data from Social Media. I have been going through the codes on Stackflow and GitHub but the machine time and processing time is very high when working on data extracted from Social Media.
Your help will be acknowledged by mentioning your name in the published manuscript on this work.
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It really depends on what you want to do. If you want to do dynamic network analysis or some kind of ERGM models, usually, having more than 500 nodes implies massive computational efforts. However, there are work arounds, e.g. using simple regression techniques. Again, it matters what you want to do.
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I´d like to test whether a priori defined edges and communities change across two severity groups of inpatients with dissociation. We seperated groups via subthreshold and matched in ratio 1:1 for age and gender to the sample of high dissociators. But how to deal with the fact that less variance can be explained in patients with low dissociation. Can we adjust matching ratio to 1:2?
happy for any help,
Philipp Göbel
#networkanalysis #networkcomparison #symptomicsframework #severitygroups
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interested
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Hi everyone,
I have a zone of water distribution system with a couple of reservoirs. I am going to manage the whole zone's valves using an Artificial Intelligence based system. I have an idea that if we can find some critical points in the zone which are very pressure sensitive about valves' changes, we can manage the whole zone's valves just based on providing the suitable pressure of these critical points. The rest points of zone would have suitable pressure because the AI model supplies the pressure of sensitive (critical) points. In the other words, the critical points would have potential for losing pressure or bursting the related pipes in the worst cases (low pressure and high pressure respectively).
However, I do not know how I can find these critical points based on hydraulic network and data mining techniques.
Do you believe that this idea would be meaningful and practical?
If yes, would you please give me some practical ideas about detecting these critical points?
Thanks in advanced
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Consider the following failure mode. A valve, which is supposed to be 75% closed (25% opened) fails in the fully open position (100% opened). In this case, a redundant valve in parallel will be useless because the redundant valve cannot reduce the flow, only a redundant valve in series with the failed valve would be able to reduce the flow.
Each valve would have to have both a parallel and series redundant valve to be able to deal with all valve failure modalities.
Regards,
Tom
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Dear all,
I would like to know if it is possible to use SAOMs (Stochastic actor oriented models) to analyse weighted networks?
Thank you in advance,
Léa DAUPAGNE
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There seems to be a less ised feature to handle ordinal values. It is discussed here: http://lists.r-forge.r-project.org/pipermail/rsiena-help/2013-July/000272.html
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I need to find TTL from Python and I found several codes but I don't know why TTL output in python different than TTL when I used ping www.google.com?
for example in python TTL = 45 or 226 ...but in command line terminal ping www.google.com TTL =118.
Do you know any python code that I obtain TTL which is matched with TTL in the command line?
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can you please share your python code ?
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Dear Researchers,
`Since I am new in the field of internet security, I need your suggestion regarding the meaning of the following features.
We have DNS google.com or youtube.com, and so on, and I want to extract different features based on Lexical and Web Scrapped.
Lexical Features:
what is the meaning of the following features? Please write with an example.
1) different ratios (different ratios (number to length, alphabet to length) ?
2) hash?
3) distance between a number to an alphabet? (You can find the meaning of these features in the paper Feature Extraction Approach to Unearth Domain Generating Algorithms (DGAs) - Page 401)
4) English domain name, not English yet pronounceable domain names, uni-gram?
Web Scrapping:
we extract information of the queried domain name from the web using Python (You can find the meaning of these features in the paper Feature Extraction Approach to Unearth Domain Generating Algorithms (DGAs) - Page 403)).
1) Levenshtein distance (sq1,se2), what is seq2?
2) Typosquat process?
Thanks
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you can use other artificial methods based on scripts that attempt to extract content from web pages HTML parsing
The use of web APIs causes complications due to robotic controls and access restrictions.
Good luck
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Hy! I analyzed data using geo databases and filtered having specific p value and log f/c values. Now I need to analyse data of Mirna and lncRNA on wgcna but I don't know how to construct network.
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I want to find motif in my PPI network but i don't know which of the cystoscope's plug-in is better .Anyone has experience with that or know any other motif detector ?
thanks
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There is a pluggin calles motif discovery in Cytoscape.
As per my experience, you can opt for this
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Hi everyone,
I am looking for some advice on what to use to perform a network analysis. Specifically, I want to evaluate the frequency/strength of connections between country collaboration on pan-European projects (i.e. Erasmus+ Projects). I already have the data set in Excel, but I do not know how to translate that to a proper network analysis or into a graph depicting these relationships.
So I am putting the question out there: what software would best and most easily allow me to do so?
Thanks!
Louis
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Dear Sir,
There are various software available for network analysis. For example, cytoscape, Pajek etc.
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Dear all,
I would like to know if it is currenly possible to use temporal ERGMs (Exponential Random Graph Models) for analyzing weighted networks?
For now, it seems that software packages available to analyse TERGMs (tergm or btergm) only use binary networks.
Thanks in advance for your answer,
Léa Daupagne
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I am planning to compile a systematic literature review. I have downloaded .csv file of a collection of papers and their respective bibliometric information (authors' names and affiliations, year of publication, keywords, references, etc.). To conduct a network analyses of this acquired data in Gephi, I need to import different spreadsheets for making nodes and edges tables. The .csv file downloaded may be used as it is for nodes (if I'm not wrong). However, I am clueless about how to make edges file from this parent .csv file to conduct different types of network analyses (e.g., based on keywords, citations, research areas, etc.). Any guidance in this regard will be highly appreciated.
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As you have already noticed, this cannot be done directly. The Scopus platform provides data as detailed data (notice that the volume of records being downloaded is intentionally limited by them) or as numerical aggregates - but there is no functionality for 'data traversal' by relationships such as co-quoting, co-authorship, etc. So you have two options - the first one is to process these data in some external analytical tool that will able to generate files for Gephi, or, the second one - to use the API provided by Gephi to create a dedicated module.
You can find an example of the first approach in:
An example of the second approach here:
but the last one is based not on Scopus but Crossref services.
But most of all, you have to do a lot of data cleaning first ;)
Good luck!
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I want to generate some nice prediction plots from my MRQAP model. I've laid out my process below, and would be very grateful to get anyone's insight, as I'm not seeing much written about this online.
I am building my own regression models on network data in R, using quadratic assignment procedure with Decker and colleagues (2007) double-semi-partialling method. In other words, I am predicting the weight of an edge given its respective node traits. This approach uses node permutations of residuals to adjust for interdependence of observations in the network. (Regression with networks involves huge heteroskedasticity, because the observations are literally connected).
Traditionally, this method (MRQAP with DSP) just produces a p-value, and original standard errors are suspect. So, I am using a Doug Altman's method to back-transform p-values into new standard errors that better reflect the actual error range (read more here; thanks to @Andrew Paul McKenzie Pegman: https://www.bmj.com/content/343/bmj.d2090). This at least allows me to make nice dot-and-whisker plots of beta coefficients and with their confidence intervals (estimate + se*.196, etc.). However, I'd still really like to make predictions.
There seem to be two logical routes to make predictions from an MRQAP model.
First, you could just make predictions normally.
This relies on your observed residuals in the model to calculate the standard error for your predictions. I think this might even work, because the homoskedasticity assumption in regression is really about covariate standard error and p-values, not prediction; this means that a heteroskedastic model can still produce solid predictions (see Matthew Drury's & Jesse Lawson's helpful notes here: https://stats.stackexchange.com/questions/303787/using-model-with-heteroskedasticity-for-predictions). However, I would love some external verification on this. Any sources I can draw on to be confident I can use this for visualizing predicted effects from networks?
Second, you could simulate the predictions, like in Zelig/Clarify.
Simulation requires building a multivariate normal distribution, where each vector has a mean of one of your model coefficients, and where the vectors share the same general correlation structure as your variance-covariance matrix. Then, you make a sample from this multi-variate distribution (eg. grab a row of observations from each vector), use these as your coefficients, and generate a set of predictions. You then repeat this about 1000 times, grabbing different sets of slightly-differing coefficients.
In other words, this approach comes with a few assumptions: 1) Your coefficients might be slightly off, but if they're wrong, they follow a normal distribution. 2) The distribution for each coefficient is related to the other coefficients in specific, empirically observed ways. 3) These distributions don't necessarily have standard deviations that reflect the nice new standard deviations generated from our DSP p-values! Ordinarily, I'd think that you'd want a multivariate normal distribution where each assumptions 1 (normal) and 2 (correlated) apply, but where you've also constrained each coefficient's distribution to reflect the standard errors from DSP. But there doesn't seem to be a good way to do this, since standard error doesn't directly factor into making a multivariate normal distribution (to my knowledge). You mostly just need the mean (coefficients) and a variance-covariance matrix.
To any kind souls out there who have read this far, what would you recommend? Should I just use normal prediction? Should I simulate with a multivariate normal distribution? Should I make some weird third multivariate-normal-distribution-that-somehow-resembles-my-standard-errors-made-indirectly-from-MRQAP-DSP?
Any thoughts would be appreciated!
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Thanks Muhammad Ali for your feedback. I'm afraid these papers don't seem to specifically answer how to handle predictions, but I could be wrong. (Dekker and colleagues' 2007 piece is certainly foundational, since they developed the technique I'm using (double-semi partialling). Any thoughts out there would still be very helpful.
Tentatively, for those interested, I've fallen on the following conclusion:
Heteroskedasticity is the big problem in network regression models. But, this is because it inflates type II error for coefficient p-values. Heteroskedasticity does not invalidate model predictions; for example, machine learning models, which are less concerned with coefficient p-values and more with prediction, do not worry about heteroskedasticity as much.
As a result, I have concluded that the standard methods should be fine. Simulations, like used in Zelig, are even better, because the multivariate normal distribution helps us adjust for sampling error too. But, as a safeguard, we probably should only present predictions when varying a coefficient that MRQAP-DSP found to be statistically significant.
Feel free to be in touch if you have thoughts about this; would love to get your input.
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Some excerpts from the article
Comparing methods for comparing networks Scientific Reports volume 9, Article number: 17557 (2019)
By Mattia Tantardini, Francesca Ieva, Lucia Tajoli & Carlo Piccard
are:
To effectively compare networks, we need to move to inexact graph matching, i.e., define a real-valued distance which, as a minimal requirement, has the property of converging to zero as the networks approach isomorphism.
we expect that whatever distance we use, it should tend to zero when the perturbations tend to zero
the diameter distance, which remains zero on a broad range of perturbations for most network models, thus proving inadequate as a network distance
Virtually all methods demonstrated a fairly good behaviour under perturbation tests (the diameter distance being the only exception), in the sense that all distances tend to zero as the similarity of the networks increases.
If achieving thermodynamic efficiency is the benchmark criterion for all kinds of networks, then their topologies should converge to the same model. If they all converge to the same model when optimally efficient, does that cast doubt on topology as a way to evaluate and differentiate networks?
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Google translation of Alyaa Khudhair Nov 2, 2020 reply:
Probably yes.
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I've been working on the network analysis of adolescent depressive symptoms. I've estimated the network, the centrality indices and network stability using packages qgraph and bootnet. Then I want to detect if there're communities or subnetworks of symptoms within the whole network. I know from the previous research that I should use package igraph. However, any function in igraph require a graph object which I don't know how to create with my raw data.
Can the network or the plot created by qgraph or bootnet transformed into the graph that igraph requires?
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Thank you so much. I figured it out. the package igraph has the function to convert a plot in qgraph package into a graph to used in igraph package.
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I am working on a project using network analysis to identify core symptoms in depression among Chinese underprivileged adolescents. 
I conducted a network comparison test between boys and girls and the results for network invariance test showed the global structure isn’t invariant (p=0.018). I would like to do an edge invariance test and I just didn’t know how to interpret the results.
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Hi all,
Can anybody suggest a "quick-and-dirty" way to summarise a measure of connectivity between polygons, based on a network of line? See the picture as an example, say that I have some districts connected by a network of roads (black lines). The red one is contiguous with both the yellow and the grey. But it has only 1 road connecting with the yellow, and 5 with the grey. Is there a clever way of summarising this? Maybe accounting also for the lenght of the roads?
Thanks in advance.
Luca
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Hi Luca,
i step 5, you can easily switch from the number of intersection to any other metrics that describe somehow the complexity of roads. Before step 4, you should calculate this metric for each of the roads.
HTH,
Ákos
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I want to consider the effect of layers similarity to solve a problem in multilayer networks. Can anyone help me which are the most important interlayer similarities in multilayer networks?
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My goal is to study the similarity famous between layers in the multiplex networks like overlap links. But I do not know which exactly the similarities between the layers are very important.
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1)cannot declare variable ‘wifiMac’ to be of abstract type ‘ns3::WifiMacHelper’
WifiMacHelper wifiMac;
^
2)In file included from ./ns3/ht-wifi-mac-helper.h:25:0,
from ./ns3/wifi-module.h:35,
from ../scratch/bcompare.cc:108:
./ns3/wifi-helper.h:75:7: note: because the following virtual functions are pure within ‘ns3::WifiMacHelper’:
class WifiMacHelper
^
3)./ns3/wifi-helper.h:85:24: note: virtual ns3::Ptr<ns3::WifiMac> ns3::WifiMacHelper::Create() const
virtual Ptr<WifiMac> Create (void) const = 0;
^
4)../scratch/bcompare.cc:1891:13: error: ‘class ns3::WifiMacHelper’ has no member named ‘SetType’
wifiMac.SetType ("ns3::AdhocWifiMac");
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Hi, me also encounter the same problem to run a previous code related with aodv routing simulation in ns3 version 3.31. Later i found there are few changes to define the physical channel and mac layer. old version syntax:
NqosWifiMacHelper wifiMac = NqosWifiMacHelper::Default ();
wifiMac.SetType ("ns3::AdhocWifiMac");
YansWifiPhyHelper wifiPhy = YansWifiPhyHelper::Default ();
YansWifiChannelHelper wifiChannel = YansWifiChannelHelper::Default ();
wifiPhy.SetChannel (wifiChannel.Create ());
WifiHelper wifi = WifiHelper::Default ();
wifi.SetRemoteStationManager ("ns3::ConstantRateWifiManager", "DataMode", StringValue ("OfdmRate6Mbps"), "RtsCtsThreshold", UintegerValue (0));
devices = wifi.Install (wifiPhy, wifiMac, nodes);
"NqosWifiMacHelper" this script is no more in new version. new syntax:
WifiHelper wifi;
YansWifiPhyHelper wifiPhy = YansWifiPhyHelper::Default ();
YansWifiChannelHelper wifiChannel;
wifiChannel.SetPropagationDelay ("ns3::ConstantSpeedPropagationDelayModel");
wifiChannel.AddPropagationLoss ("ns3::FriisPropagationLossModel");
wifiPhy.SetChannel (wifiChannel.Create ());
// Add a mac and disable rate control
WifiMacHelper wifiMac;
wifiMac.SetType ("ns3::AdhocWifiMac");
wifi.SetRemoteStationManager ("ns3::ConstantRateWifiManager", "DataMode", StringValue ("OfdmRate6Mbps"), "RtsCtsThreshold", UintegerValue (0));
devices = wifi.Install (wifiPhy, wifiMac, nodes);
Then I can successfully run the code. hope this may help to new users like me. It almost took 1 night for me to find the problem as there were no specific solution in internet for this. good luck.
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Dear peers,
I am working with extinction models in interaction networks using the bipartite R-package.
I can determine the order in which species will be removed based on abundance and degree or random.
For example:
#####
data(Safariland)
abundance <- second.extinct(Safariland, participant = "lower", method = "abundance", nrep = 10,
details = FALSE, ext.row=NULL, ext.col=NULL)
robustness(abundance)
slope.bipartite(abundance)
#####
However, I need and am not able to elaborate a vector to determine a different extinction sequence, using the ‘external’ method.
Thanks
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Dear, Steffen,
Many thanks for the answer!
I got it.
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The primary focus is to perform a miRNA-miRNA synergistic network analysis, with the goal to predict / identify miRNA pairs that might have a high probability of regulating a pathway or a set of pathways in a miRNA-miRNA network based on shared target genes.
It would be great if you can suggest some good resources to get started with network analysis, and significance of networks in biology with context to miRNA networks.
Thanks!
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4 Best Network Analysis Courses & Classes [2020]
1. Introduction to Network Analysis in Python (DataCamp)
2. Network Analysis in R (DataCamp)
3. Network Analysis in the Tidyverse (DataCamp)
4. Network Analysis Courses (Coursera)
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What are the methods used to assess the robustness of network with flow? How to model the flow (discrete entities with origin-destination routes) in a network.
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Can we say that robustness = size of the largest connected component/size of the network? Apparently we need to see the result of the robustness after several attacks.
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I am a physician and visiting research scientist at yale and together with my coauthors have published several studies in the field of psychology through Network Modeling and related analyses using r packages like bootnet, qgraph, NetworkComparisonTest, etc. I thought it might be a good idea to discuss different subjects related to this field, in a group. I am also interested in collaboration with other teams working in the field. Let's share our ideas, questions and suggestions in this group.
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Makes sense. Thanks for letting me know.
I hope followers of this discussion forum check your study and package,
which address an interesting topic in network analysis. Let's keep in touch!
Best Wishes,
Farhad
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I'm currently trying to learn how to use network analysis, as this method of analysis is increasingly used in psychiatry and psychology research. But as the question suggests, I'm very much a frog in the well regarding this topic. When looking for sources online, most would suggest about "use WCGNA", "use r-package," "use bayesian program," or other similar measures.
However, if I look at a glance, most of the tools are mainly used for good visualization. As long as we can define centralized nodes, know the value of r for each two nodes, differentiating direct/indirect correlation, and draw the lines with thickness corresponding to r-value, we should be able to make network analysis without a program.
Is it wrong? Is there any good resources to learn from scratch?
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Hi Afkar, I don't think there are any quick solutions. If you plan to explore network analysis, I suggest taking the time to learn the theory behind it and a program that can help you reach your goals. Gephi has a user-friendly interface for modelling and analyzing networks, with many online tutorials, blog posts, and a facebook support group to help along the way. https://gephi.org/ https://gephi.org/users/quick-start/ Good luck!
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Im looking for research that uses position generator measures of social capital, developed by Lin & Dumin (1986), or similar information (social ties on a set of predefined occupations) using software specifically designed for network analysis (Ucinet mainly).
Thanks!
Lin, N., & Dumin, M. (1986). Access to occupations through social ties. Social Networks, 8(4), 365-385
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I need to establish if there is a link between 2 columns from two different datasets with one matching column, where;
Dataset1: bipartite: (M, DS)
M DS
m23 ds3
m23 ds67
m54 ds325
... ...
Dataset2: tripartite: (M, G, DG)
M G DG
m23 g6 dg32
m23 g8 dg1
m54 g32 dg65
... ... ...
These 2 datasets have one column in common(i.e., **M**), and the relationship among the elements is shown below:
```
M ----affects----> G
M ----causes-----> DS
DG ----affects----> M
```
Primary Goal: To calculate the probability of a possible link/edge that might exist between indirectly related columns(eg. **DG** and **DS**) via the common column(**M**).
So, for a given list of DS entries, how to find the probability of the existence of a link/edge between
selected DS, and all the other DGs
```
DS <---- ----> DG
```
If DS; (ds3, ds67) were selected, the output should be like this:
element1 - element2 - probability/statistical value to signify the existence of direct relationship OR link.
```
ds3 - dg32 - 100% (common M value)
ds3 - dg1 - 100% (common M value)
ds3 - dg65 - 43.66%
---
ds67 - dg32 - 100% (common M value)
ds67 - dg1 - 100% (common M value)
ds67 - dg65 - 55.12%
```
I am trying to code this in Java, but Python based solutions can work too.
I am sorry I am not too familiar with graph theory, a little descriptive solutions would be really appreciated.
Thanks.
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I have 14 miRNA that is related to a particular disease. I want to draw a network like Gene Networking (GeneMania).I can draw a network easily by inputting the gene name in genemania but which softwere can take input miRNA name like this? Which software is better? I was trying to use Cytoscape but it require pre-networking data (if I am not wrong). I am not sure whether I can get any pre-networking data for miRNA. Some of the miRNA is quite new and some old version of the software can't recognize that one.
Please help me how I can get a network like Genemania. I only can input different miRNA name and particular disease. Thanks.   
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We recently developed miRViz to interpret microRNA datasets using microRNA networks:
To build miR-mRNA network, a Canadian group has developed miRNet: https://www.mirnet.ca/miRNet/home.xhtml
Both may be useful for you. No need for computational skills. I would suggest first miRViz, and then miRNet.
If you want more information, we also published in 2015 a paper building microRNA networks (we use these networks in miRViz):
'hope this will help you.
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I would like to track the presence of some ideas in papers in economics, and I have been reading about citation network analysis and I have found some datasets (like the https://www.aminer.cn/citation, which contains 4 million papers, but about 25 thousand from journals that interests me). Can I find a freely accessible dataset with more papers, specifically in Economics? Besides that, I would have to do some group identification (community identification), and so far the best reference I found is a paper by Clauset et. al., "Finding community structure in very large networks". (https://arxiv.org/abs/cond-mat/0408187v2 ). A completely different approach would be having as many papers as possible from many years, and do some type of text analysis, but I am assuming that getting this kinda of data is still more difficult, so I am trying the first approach). I appreciate any possible help.
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A lot depends on how you want to narrow down the data set (time period, magazine, subject matter) and whether the data obtained allows you to build a citation network at all. Depending on the expected volume of data, you can use the approach to extract all records and then in the analytical tool delete records not related to the topic, or extract records from databases that allow you to narrow the set at the stage of creating queries that include individual fields (including title or keywords ).
To easily start your adventure you can use the Gephi application plugin that automates the process of downloading data from Crossref:
Here you can watch it in action:
You can also use other databases that allow you to download search results as files. E.g. Scopus.
The last one is not free, but probably as a student, you may access it at your library.
Cheers!
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I performed a differential expression analysis and I have a list of DE human genes. now, I want to visualize DEGs by Cytoscape (showing up-regulated and down-regulated proteins with different shapes and set the size of the nods on the base of levels of expression.) but this work needs a network and expression data.how should I obtain these files? And after that how to connect them to build a network?
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Hello Momeni, I got what you want, you follow this questions and answers. It will help you.
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Hello wveryone.
I'd like to perform some centrality measures that are not covered by igraph but CINNA library does. Would you endorse the package on the base of your experience?
Thanks a lot.
Stefano
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Hi,
if you have any questions or need any help,
you are welcome to ask me or the CINNA's maintainer Minoo Ashtiani
for more details, check:
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The theorem states that the reactance of a passive, lossless two-terminal (one-port) network always strictly monotonically increases with frequency. Can this theorem be extended to two port circuit parameters like mutual impedance etc.?
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I have found some datasets captured on the border router of an orgnization (e.g., The CTU-13 Dataset, http://mcfp.weebly.com/the-ctu-13-dataset-a-labeled-dataset-with-botnet-normal-and-background-traffic.html), but these data contain few internal connections within the organization.
So, could you please give me some advice about where to find a network dataset of an organization with internal connection data?
Many thanks for your time!
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Hey , I'm looking for IoT network traffic datasets having MQTT, CoAP , HTTP protocols. Kindly, let me know.
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I need to do protein-protein interaction network analysis for which dataset was downloaded from GEO datasets. Data is in the .cel format. I am unable to read these files. Please also suggest "How to apply gcrma package on data?"
I have GSM358670 in .cel format and I am getting an error like
read.celfile(GSM358670)
Error in read.celfile(GSM358670) :
STRING_ELT() can only be applied to a 'character vector', not a 'list'
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Hi
Firstly, you need to install several R packages, including "affyPLM" and "affy".
R code (To install packages):
###############
biocLite("affy")
biocLite("affyPLM")
###############
Then, you should put all the .cel files into one folder and set the folder as the work directory in R environment.
Finally, load the two R packages and process the .cel files.
R code (load the packages and process the .cel files):
################
library(affyPLM)
library(affy)
Data<-ReadAffy()
sampleNames(Data)
N=length(Data)
eset.rma<-rma(Data)
groupA_exprs<-exprs(eset.rma)
probeid<-rownames(groupA_exprs)
groupA_exprs<-cbind(probeid,groupA_exprs)
write.table(groupA_exprs,file="tumor.expres.txt",sep='\t',quote=F,row.names=F)
#################
The .txt file is the gene expression matrix.
Good luck.
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I am working with nematode and host Medicago. I have transcriptome data for both species and I also have a list of differentially expressed genes(DEG). Now I would like to see if DEG of host and nematode are associated by calculating a correlation between genes. Which package should I use? I am new in this area so please give me suggestions on network analysis, steps, packages, papers. Thank you!
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Dear Shova
In this case Your observation points are time-points. And have to say, six - is not an optimal number for correlation analysis, but anyway - yes, the data organization You wrote is correct. Just switch row-column view, because, as far as I remember, "corr.test" recognizes observation points as rows. Although, I may be wrong with this...
Another thing I would mention: if You plan to include for correlation not all genes, but only those that are DE at any time-point, it can be complicated to interpret.
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I have already found some reference authors who model some parts of the system, for example, sensor, transceivers, link, propagation space, the network itself and, sometimes, putting it all together, but they are somewhat limited because they do not constitute a global model confronted with reality.
There is a lack of information. Today's models are useful for their purposes, but I'd like to know more about real-world cases, such as smartwatches that communicate with our mobile phone apps and a complete AI network set up to manage our daily lives. Is there any academic model for this?
I am putting this here to perhaps start a debate, trying to understand how technology can help our quality of life. And how the models, more precisely the energy efficiency ones, were modeled and how they are put into practice. Or today we live in an ad hoc scenario, where things become useful and overcome each other by trade advantages and convenience only.
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You can use wsn with iot some softwares with encryptions systems like AES also combined with arduinio for sending and receiving.
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Usually in many contexts, while substituting, it is assumed z=e^jw and s=jw (w=frequency). But actually, z=r*e^jw and s=σ + jw. Why do we assume r=1 and σ=0 always?
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This question concerns the relation between the Z transform and the Laplace S transform. It is so that the z-Transform is the discrete time Laplace transform.
Please follow this proof:
F(S) = Integral f(t) exp -St dt from 0 to infinity.
Let us descretize t such t= nTs with Ts is the sampling time and and is the sampling instant. Ts=1/fs with fs is the sampling frequency.
Substituting the descretizing condition in the Laplace transform ,then we have:
F(S) = SUM f(nTs) exp - n S Ts
Now one can define F(z) as z= exp STs,
F(z) = SUM f(nTs) z^-n
The last equation is the z transform of the discrete time function f(nTs)
In order to map the z-plane one has to locate the jw axis of the S -plane on the Z-plane where sigma=0.
It follows z at the jw axcess = expjwTs,
So as a complex quantity the magnitude of z =1 and its angle =wTs= 2pif/fs
which is called normalized radian frequency.
So the line corresponds to jw axis in the S plane is a circle whose amplitude is eqaul to one and it is called the unity circle.
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