help > Small-world network properties & Network edges options
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May 28, 2018  10:05 PM | Panagiotis Fotiadis - Massachusetts General Hospital
Small-world network properties & Network edges options
Hello,

I just started using CONN (version 18.a) and wanted to thank you for designing such a user-friendly and powerful software!

I am trying to explore the resting state functional connectivity differences between two groups (one diseased group: 16 subjects, and one control group: 14 subjects), and I had a few questions:

1) Is there a way to see/define whether the brain of each subject obeys small-world network properties (for instance by looking at the average path length and clustering coefficients)? 

2) Also, I am a little confused about the 'Network edges (adjacency matrix threshold)' options in the 'graph theory results explorer' GUI: If I decide to use 'cost' (the default setting) with a value of 0.15, how would I explain to the potential reviewers why I chose that particular threshold for my analyses? Is there something in the adjacency matrix that could point me to that?


I apologize for the potential triviality of the questions, and thank you in advance for your time!

Best,
Panos
May 31, 2018  08:05 AM | Panagiotis Fotiadis - Massachusetts General Hospital
RE: Small-world network properties & Network edges options
Hello,

Just wanted to re-circulate this, in case someone had some feedback!

Thanks again,
Panos

Originally posted by Panagiotis Fotiadis:
Hello,

I just started using CONN (version 18.a) and wanted to thank you for designing such a user-friendly and powerful software!

I am trying to explore the resting state functional connectivity differences between two groups (one diseased group: 16 subjects, and one control group: 14 subjects), and I had a few questions:

1) Is there a way to see/define whether the brain of each subject obeys small-world network properties (for instance by looking at the average path length and clustering coefficients)? 

2) Also, I am a little confused about the 'Network edges (adjacency matrix threshold)' options in the 'graph theory results explorer' GUI: If I decide to use 'cost' (the default setting) with a value of 0.15, how would I explain to the potential reviewers why I chose that particular threshold for my analyses? Is there something in the adjacency matrix that could point me to that?


I apologize for the potential triviality of the questions, and thank you in advance for your time!

Best,
Panos
Jun 5, 2018  06:06 AM | Alfonso Nieto-Castanon - Boston University
RE: Small-world network properties & Network edges options
Hi Panos,

Your two questions are related. You can of course always justify the choice of threshold from previous studies, but one relatively simple way to justify the choice of cost threshold from your data is to find which threshold value results in networks that seem to follow "small-world" properties (i.e. comparatively high global efficiency compared to lattices, and comparatively high local efficiency compared to random graphs). In CONN graph-theory GUI you may simply delete the threshold value in the "adjacency matrix threshold" field, and that will create a small plot that shows the network global and local efficiency for different cost threshold values (and also for reference the global and local efficiency values for the same cost threshold values for random graphs and regular graphs / lattices). Choosing a threshold value that seems to jointly maximize the difference between global efficiency of your networks (compared to lattices) as well as the local efficiency of your networks (compared to random graphs) is a common/reasonable approach (and the default cost=.15 value typically is close to this "optimal" level for medium-size networks).

In case this helps, I am also attaching a patch that will create an additional plot to the above display showing you directly GE_data-GE_lattice+LE_data-LE_random for each threshold value, to perhaps more directly/intuitively justify the choice of threshold value using this approach (this patch is for 18a, to install it simply copy the attached file to your conn distribution folder overwriting the file with the same name there)
 
Hope this helps
Alfonso
Originally posted by Panagiotis Fotiadis:
Hello,

I just started using CONN (version 18.a) and wanted to thank you for designing such a user-friendly and powerful software!

I am trying to explore the resting state functional connectivity differences between two groups (one diseased group: 16 subjects, and one control group: 14 subjects), and I had a few questions:

1) Is there a way to see/define whether the brain of each subject obeys small-world network properties (for instance by looking at the average path length and clustering coefficients)? 

2) Also, I am a little confused about the 'Network edges (adjacency matrix threshold)' options in the 'graph theory results explorer' GUI: If I decide to use 'cost' (the default setting) with a value of 0.15, how would I explain to the potential reviewers why I chose that particular threshold for my analyses? Is there something in the adjacency matrix that could point me to that?


I apologize for the potential triviality of the questions, and thank you in advance for your time!

Best,
Panos
Attachment: conn_network.m
Jun 5, 2018  08:06 AM | Panagiotis Fotiadis - Massachusetts General Hospital
RE: Small-world network properties & Network edges options
Hi Alfonso,

Thank you for the detailed response and the patch! I had two follow-up questions:

1) Since I am comparing two groups is there a way (or does it even make sense) to calculate a measure that reflects their small-world propensity (or their small-"worldness")? I was thinking something like the small coefficient sigma (defined as (C/C_r)/(L/L_r), where C is the clustering coeff. of my network, C_r is the clustering coeff. of an equivalent random network, L the average path length of my network, and L_r the average path length of an equivalent random network), or any other measure that you might have in mind. Even though I know how to look up the clustering coeff. and average path length parameters of each subject, I didn't know how to calculate the same measures for an equivalent random network. 

2) Also, am I correct to assume that the ROI.mat that is saved under the secondlevel tab of my results is the binary connectivity matrix of the ROI-to-ROI correlations of the analysis that I have specified (i.e. diseased group vs control group)? And if it is, is there a way to plot said brain connectivity matrix?

Thanks again for your time and comments!
Panos

Originally posted by Alfonso Nieto-Castanon:
Hi Panos,

Your two questions are related. You can of course always justify the choice of threshold from previous studies, but one relatively simple way to justify the choice of cost threshold from your data is to find which threshold value results in networks that seem to follow "small-world" properties (i.e. comparatively high global efficiency compared to lattices, and comparatively high local efficiency compared to random graphs). In CONN graph-theory GUI you may simply delete the threshold value in the "adjacency matrix threshold" field, and that will create a small plot that shows the network global and local efficiency for different cost threshold values (and also for reference the global and local efficiency values for the same cost threshold values for random graphs and regular graphs / lattices). Choosing a threshold value that seems to jointly maximize the difference between global efficiency of your networks (compared to lattices) as well as the local efficiency of your networks (compared to random graphs) is a common/reasonable approach (and the default cost=.15 value typically is close to this "optimal" level for medium-size networks).

In case this helps, I am also attaching a patch that will create an additional plot to the above display showing you directly GE_data-GE_lattice+LE_data-LE_random for each threshold value, to perhaps more directly/intuitively justify the choice of threshold value using this approach (this patch is for 18a, to install it simply copy the attached file to your conn distribution folder overwriting the file with the same name there)
 
Hope this helps
Alfonso
Originally posted by Panagiotis Fotiadis:
Hello,

I just started using CONN (version 18.a) and wanted to thank you for designing such a user-friendly and powerful software!

I am trying to explore the resting state functional connectivity differences between two groups (one diseased group: 16 subjects, and one control group: 14 subjects), and I had a few questions:

1) Is there a way to see/define whether the brain of each subject obeys small-world network properties (for instance by looking at the average path length and clustering coefficients)? 

2) Also, I am a little confused about the 'Network edges (adjacency matrix threshold)' options in the 'graph theory results explorer' GUI: If I decide to use 'cost' (the default setting) with a value of 0.15, how would I explain to the potential reviewers why I chose that particular threshold for my analyses? Is there something in the adjacency matrix that could point me to that?


I apologize for the potential triviality of the questions, and thank you in advance for your time!

Best,
Panos
Jul 12, 2018  02:07 PM | Panagiotis Fotiadis - Massachusetts General Hospital
RE: Small-world network properties & Network edges options
Hi Alfonso,

Just wanted to re-circulate this. Thanks again for your time and help!

Best,
Panos
Originally posted by Panagiotis Fotiadis:
Hi Alfonso,

Thank you for the detailed response and the patch! I had two follow-up questions:

1) Since I am comparing two groups is there a way (or does it even make sense) to calculate a measure that reflects their small-world propensity (or their small-"worldness")? I was thinking something like the small coefficient sigma (defined as (C/C_r)/(L/L_r), where C is the clustering coeff. of my network, C_r is the clustering coeff. of an equivalent random network, L the average path length of my network, and L_r the average path length of an equivalent random network), or any other measure that you might have in mind. Even though I know how to look up the clustering coeff. and average path length parameters of each subject, I didn't know how to calculate the same measures for an equivalent random network. 

2) Also, am I correct to assume that the ROI.mat that is saved under the secondlevel tab of my results is the binary connectivity matrix of the ROI-to-ROI correlations of the analysis that I have specified (i.e. diseased group vs control group)? And if it is, is there a way to plot said brain connectivity matrix?

Thanks again for your time and comments!
Panos

Originally posted by Alfonso Nieto-Castanon:
Hi Panos,

Your two questions are related. You can of course always justify the choice of threshold from previous studies, but one relatively simple way to justify the choice of cost threshold from your data is to find which threshold value results in networks that seem to follow "small-world" properties (i.e. comparatively high global efficiency compared to lattices, and comparatively high local efficiency compared to random graphs). In CONN graph-theory GUI you may simply delete the threshold value in the "adjacency matrix threshold" field, and that will create a small plot that shows the network global and local efficiency for different cost threshold values (and also for reference the global and local efficiency values for the same cost threshold values for random graphs and regular graphs / lattices). Choosing a threshold value that seems to jointly maximize the difference between global efficiency of your networks (compared to lattices) as well as the local efficiency of your networks (compared to random graphs) is a common/reasonable approach (and the default cost=.15 value typically is close to this "optimal" level for medium-size networks).

In case this helps, I am also attaching a patch that will create an additional plot to the above display showing you directly GE_data-GE_lattice+LE_data-LE_random for each threshold value, to perhaps more directly/intuitively justify the choice of threshold value using this approach (this patch is for 18a, to install it simply copy the attached file to your conn distribution folder overwriting the file with the same name there)
 
Hope this helps
Alfonso
Originally posted by Panagiotis Fotiadis:
Hello,

I just started using CONN (version 18.a) and wanted to thank you for designing such a user-friendly and powerful software!

I am trying to explore the resting state functional connectivity differences between two groups (one diseased group: 16 subjects, and one control group: 14 subjects), and I had a few questions:

1) Is there a way to see/define whether the brain of each subject obeys small-world network properties (for instance by looking at the average path length and clustering coefficients)? 

2) Also, I am a little confused about the 'Network edges (adjacency matrix threshold)' options in the 'graph theory results explorer' GUI: If I decide to use 'cost' (the default setting) with a value of 0.15, how would I explain to the potential reviewers why I chose that particular threshold for my analyses? Is there something in the adjacency matrix that could point me to that?


I apologize for the potential triviality of the questions, and thank you in advance for your time!

Best,
Panos
Jul 12, 2018  03:07 PM | Alfonso Nieto-Castanon - Boston University
RE: Small-world network properties & Network edges options
Hi Panos,

Regarding (1), sorry there is no simple way to generate those C_r and L_r values in CONN. You may do that "manually" by creating random graphs with the same number of nodes and edges and then using the function conn_network_measures to compute the C and L values. That said, in this particular case, that may not be necessary since we are using the same cost threshold value across all subjects, so all of the individual-subject graphs will have the same number of nodes and edges and both C_r and L_r measures will be exactly the same for every subject (and also across the two groups). That means that you can safely disregard those constant terms and compare directly the C/L measure between your two groups (and get exactly the same statistics as if you were comparing the (C/C_r)/(L/L_r) measures). 

Regarding (2), the ROI.mat file contains all individual ROI-to-ROI second-level results, in this case it may be simpler to use the "export adjacency matrices" button in CONN's graph theory results explorer. That will create a file directly containing the binary connectivity matrices for every subject (and for every condition if you have multiple conditions in your analysis). For plotting purposes, the default display in that same GUI will show you the average connectivity matrix across all subjects included in your selected second-level analysis (and you may right-click on the brain display and select "display 3d view" for a higher-resolution version of this display with a few more print options). Alternatively you may see this post (https://www.nitrc.org/forum/message.php?...) if you prefer to manually create this sort of plots. 

Hope this helps
Alfonso 


Originally posted by Panagiotis Fotiadis:
Hi Alfonso,

Just wanted to re-circulate this. Thanks again for your time and help!

Best,
Panos
Originally posted by Panagiotis Fotiadis:
Hi Alfonso,

Thank you for the detailed response and the patch! I had two follow-up questions:

1) Since I am comparing two groups is there a way (or does it even make sense) to calculate a measure that reflects their small-world propensity (or their small-"worldness")? I was thinking something like the small coefficient sigma (defined as (C/C_r)/(L/L_r), where C is the clustering coeff. of my network, C_r is the clustering coeff. of an equivalent random network, L the average path length of my network, and L_r the average path length of an equivalent random network), or any other measure that you might have in mind. Even though I know how to look up the clustering coeff. and average path length parameters of each subject, I didn't know how to calculate the same measures for an equivalent random network. 

2) Also, am I correct to assume that the ROI.mat that is saved under the secondlevel tab of my results is the binary connectivity matrix of the ROI-to-ROI correlations of the analysis that I have specified (i.e. diseased group vs control group)? And if it is, is there a way to plot said brain connectivity matrix?

Thanks again for your time and comments!
Panos

Originally posted by Alfonso Nieto-Castanon:
Hi Panos,

Your two questions are related. You can of course always justify the choice of threshold from previous studies, but one relatively simple way to justify the choice of cost threshold from your data is to find which threshold value results in networks that seem to follow "small-world" properties (i.e. comparatively high global efficiency compared to lattices, and comparatively high local efficiency compared to random graphs). In CONN graph-theory GUI you may simply delete the threshold value in the "adjacency matrix threshold" field, and that will create a small plot that shows the network global and local efficiency for different cost threshold values (and also for reference the global and local efficiency values for the same cost threshold values for random graphs and regular graphs / lattices). Choosing a threshold value that seems to jointly maximize the difference between global efficiency of your networks (compared to lattices) as well as the local efficiency of your networks (compared to random graphs) is a common/reasonable approach (and the default cost=.15 value typically is close to this "optimal" level for medium-size networks).

In case this helps, I am also attaching a patch that will create an additional plot to the above display showing you directly GE_data-GE_lattice+LE_data-LE_random for each threshold value, to perhaps more directly/intuitively justify the choice of threshold value using this approach (this patch is for 18a, to install it simply copy the attached file to your conn distribution folder overwriting the file with the same name there)
 
Hope this helps
Alfonso
Originally posted by Panagiotis Fotiadis:
Hello,

I just started using CONN (version 18.a) and wanted to thank you for designing such a user-friendly and powerful software!

I am trying to explore the resting state functional connectivity differences between two groups (one diseased group: 16 subjects, and one control group: 14 subjects), and I had a few questions:

1) Is there a way to see/define whether the brain of each subject obeys small-world network properties (for instance by looking at the average path length and clustering coefficients)? 

2) Also, I am a little confused about the 'Network edges (adjacency matrix threshold)' options in the 'graph theory results explorer' GUI: If I decide to use 'cost' (the default setting) with a value of 0.15, how would I explain to the potential reviewers why I chose that particular threshold for my analyses? Is there something in the adjacency matrix that could point me to that?


I apologize for the potential triviality of the questions, and thank you in advance for your time!

Best,
Panos