Analysis - Reciprocal trust, distrust and asymmetries + all trust all subgraphs

[DdmrDdmr]

1. Introduction

I was curious what trust relations looked like from the reciprocal point of view, with all the combinations between them. Now that I could sum up a little time for it, I gave it a go, wanting to specifically answer:

-   How many people trust each other mutually?
-   How many people distrust each other mutually?
-   How many people distrust each other asymmetrically? (i.e. A trusts B but B distrusts A, or vice-versa).
-   Who are the top reciprocal trusted /distrusted forum members.

To give it all a context, the overall Custom Trust Networks have the following gross related numbers which I keep track of weekly (see Customized Trust Network – Interactive tool to see who we trust/distrust).
 

Code:

Date                Trust/Dist. rel.    Trust rel.          Distrust rel.       Customized Lists    Distinct Trusted/Untrusted
09/02/2019          31450               25710               5740                4145                8855
02/02/2019          31238               25392               5846                4123                8811
26/01/2019          25777               22083               3694                4083                8707
19/01/2019          25387               21811               3576                4052                8662
12/01/2019          23800               20720               3080                3957                8498
05/01/2019          22605               19637               2968                3891                8527

Note: some of the trust networks are recent, and some really old and possibly stale. Since there is no associated date, I cannot use the date as an additional analytical dimension.


2. Reciprocal Trust relations

There are 3.770 reciprocal trust relations. Since each of these reciprocal trust relations is between two different people, that means that there are 1.885 pairs of people that mutually trust each other.
The 3.770 reciprocal trust relations represent 13,11% of the 25.710 positive trust relations.

For example, currently, I’m on a "reciprocal Trust relationship" (don’t get me wrong there) with two forum members out of my short and experimental Personal Trust List.

A complete list can be found here (first tab): https://docs.google.com/spreadsheets/d/1oI11POXylBm6UqjFeb9JOkxXp2XkN4s9yMKp8To6nrQ/edit?usp=sharing

These are the top 25 forum members with most reciprocal positive Trust relations:

Code:

R1UserfromName                                    nReciprocalRel nTotalRel % Reciprocal
CanaryInTheMine                                   41             247       16,60%
Sampey                                            35             228       15,35%
suchmoon                                          32             95        33,68%
owlcatz                                           24             95        25,26%
BitcoinPenny                                      24             80        30,00%
TMAN                                              23             117       19,66%
OgNasty                                           20             91        21,98%
The Pharmacist                                    20             45        44,44%
xtraelv                                           20             85        23,53%
greenplastic                                      19             51        37,25%
Lauda                                             19             63        30,16%
zazarb                                            18             28        64,29%
theymos                                           18             67        26,87%
qwk                                               18             35        51,43%
Kaznachej123                                      17             24        70,83%
willi9974                                         17             73        23,29%
marlboroza                                        17             52        32,69%
Lafu                                              16             59        27,12%
KWH                                               15             146       10,27%
Thule                                             15             307       04,89%
yogg                                              15             47        31,91%
PsychoticBoy                                      15             91        16,48%
tmfp                                              15             40        37,50%
Deena                                             15             307       04,89%
Coolcryptovator                                   14             24        58,33%	 

A complete list can be found here (second tab): https://docs.google.com/spreadsheets/d/1oI11POXylBm6UqjFeb9JOkxXp2XkN4s9yMKp8To6nrQ/edit?usp=sharing


3. Reciprocal Distrust relations

There are only 482 reciprocal distrust relations, corresponding to 241 pairs of people that mutually distrust each other. That seems pretty low with all that is going on.
The 480 reciprocal trust relations represent 8,40% of the 5.740 negative trust relations.

A complete list can be found here (third tab): https://docs.google.com/spreadsheets/d/1oI11POXylBm6UqjFeb9JOkxXp2XkN4s9yMKp8To6nrQ/edit?usp=sharing

These are the top 25 forum members with most reciprocal Distrust relations:

Code:

R1UserfromName                                    nReciprocalRel nTotalRel % Reciprocal			
cryptohunter                                      22             51        43,14%			
owlcatz                                           20             95        21,05%			
OgNasty                                           19             91        20,88%			
Timelord2067                                      18             135       13,33%			
Foxpup                                            17             64        26,56%			
peloso                                            16             27        59,26%			
LFC_Bitcoin                                       16             58        27,59%			
Quickseller                                       13             84        15,48%			
Lauda                                             12             63        19,05%			
TMAN                                              12             117       10,26%			
TECSHARE                                          12             105       11,43%			
Thule                                             11             307       03,58%			
xtraelv                                           11             85        12,94%			
suchmoon                                          9              95        09,47%			
Hhampuz                                           9              57        15,79%			
TheNewAnon135246                                  7              38        18,42%			
Bazinga442                                        7              307       02,28%			
marlboroza                                        7              52        13,46%			
Deena                                             7              307       02,28%			
defcon23                                          6              74        08,11%			
mocacinno                                         6              46        13,04%			
TheFuzzStone                                      6              21        28,57%			
H8bussesNbicycles                                 6              308       01,95%			
dogie                                             6              29        20,69%			
Tomatocage                                        6              48        12,50%		

A complete list can be found here (fourth tab): https://docs.google.com/spreadsheets/d/1oI11POXylBm6UqjFeb9JOkxXp2XkN4s9yMKp8To6nrQ/edit?usp=sharing


4. Asymmetrical Trust/Distrust relations

There are only 116 asymmetrical trust relations, corresponding to 58 pairs of people where one trusts another, but is distrusted back. That may change when they see that fact on the below provided list…

A complete list can be found here (fith tab): https://docs.google.com/spreadsheets/d/1oI11POXylBm6UqjFeb9JOkxXp2XkN4s9yMKp8To6nrQ/edit?usp=sharing


5. In short
I had no idea what the resulting figures would be until I did the above exercise. The fact that only 13,11% of positive trust relationships are mutual is a bit below what I would have guessed, since I would have expected more "collusion" on that front (of course, looking over the provided lists on a per user case may highlight some cases).
The 8,40% of negative trust relationships that are mutual are possibly rather reprisal related, although who knows, and really it should be looked at on a case by case basis.
The asymmetries are rather insignificant in number, and therefore not really representative.


Side note:
I started off thinking that Trust was all related to the business side of things, and had that area of confinement as a centrepiece when looking over trust rates. I think that was the original idea, and as such, delimits in an easier manner the visual interpretation of the Trust figures on the user’s profile.
 
The fact that my initial assumption (from months ago) is not so, and that Trust extends to multiple fields, with diverse conceptual and often subjective application criteria, make the reading of the feedback the means of interpreting the trust scores on one profile, which is more cumbersome that just looking at them to understand a trade related concept.
 

[Quickseller]

Interesting data.

I would be curious to see any patterns of trust circles in which a group of people all trust each other.

[LoyceV]

-   How many people distrust each other asymmetrically? (i.e. A trusts B but B distrusts A, or vice-versa).

Can we call them backstabbers?

Seriously though, I think this category is the most interesting one.

These are the top 25 forum members with most reciprocal Distrust relations:

Code:

R1UserfromName                                    nReciprocalRel nTotalRel % Reciprocal			
cryptohunter                                      22             51        43,14%	

He must be so happy to finally be on top of a list

4. Asymmetrical Trust/Distrust relations

There are only 116 asymmetrical trust relations, corresponding to 58 pairs of people where one trusts another, but is distrusted back. That may change when they see that fact on the below provided list…

I would have expected more than 58 pairs, considering how many I found already without searching for them. Trusting someone's judgement even though he doesn't trust yours is kinda ironic, but also shows good use of the trust list without being influenced by personal quarrels.

[DdmrDdmr]

<…>I would be curious to see any patterns of trust circles in which a group of people all trust each other.

That’s a nice one to try out, although pretty tough on SQL. I may try to see if I can get it done (I think I’ve got the conceptual algorithm, but implementing it is not too easy).

<…> I would have expected more than 58 pairs, considering how many I found already without searching for them.

I couldn’t make out anymore with last Saturday’s data (unless I messed up somewhere …).

307 is the number to avoid.

I’m still trying to break the code ..

[LoyceV]

<…> I would have expected more than 58 pairs, considering how many I found already without searching for them.

I couldn’t make out anymore with last Saturday’s data (unless I messed up somewhere …).

I count to the same number of backstab-relations (full data is quite messy).

[DdmrDdmr]

<...> I count to the same number of backstab-relations <...>

Ok, good, seems that I got it right then. 

On another note, it could be interesting to derive what @Quickseller suggested. It’s rather more complex although I believe I did do something of the kind with merit a long time ago (but never published it). I’ll take a look into it if I can at some point.

[OgNasty]

You should add in % of total positive or negative trust ratings so there’s some context.

Edit:  Sorry, was browsing on my mobile and it got cut off.

[DdmrDdmr]

<...>

I did: It's the nTotalRel column, so the % that shows on the nominal lists is based on the number of reciprocal relations out of all the number of forum members trusted or distrusted by a given person.

For example, I show as:

R1UserfromName   nReciprocalRel   nTotalRel   % Reciprocal
DdmrDdmr                   2                11            18,18%

-> I have reciprocal trust with 2 forum members (18,18%) out of the 11 in my trust/distrust customized (experimental) list.

[LFC_Bitcoin]

Interesting data.

I would be curious to see any patterns of trust circles in which a group of people all trust each other.

Well I can tell you one. Most of the posters here ——> https://bitcointalk.org/index.php?topic=5103988.0

It’s likely that many of them are alts

[DdmrDdmr]

<…> I would be curious to see any patterns of trust circles in which a group of people all trust each other.

Something like this:

If I detected it properly, there is a complete Trust subgraph between CanadaBits, Funny, gyscam leancuisine, Operatr, P4ndoraBox7, tennozer. It’s a case of 7 accounts that all seem to trust each other.

Edit: Better representation using the new tool I created for this excercise:
https://fusiontables.google.com/DataSource?docid=18y8mSJwCj7jWpaVGZoVFyXE4WpSPaaQQTJr_3Uf0#chartnew:id=3




I’m creating an algorithm to find all the subgraphs, but it’s not complete yet. The above case is the one with most accounts trusting each other that I have found, but as I said, this is (tough) work in progress and I may not succeed in finding all the complete node subgraphs.

The chart above is manually parametrized from the subgraph I detected. Canadabits appears in blue for some reason I cannot yet grasp.

I took this on as a personal challenge, and there is no intention on judging the actual implied. For all I know, they all trust each other and patrol their domains in good spirit. Actually, none of them have been active for some time now that I’ve taken a peak into the implied accounts.

[Jet Cash]

I feel so out of it. I don't think I am in any trust or merit circles.

I guess I'm just an old fashioned square.

[suchmoon]

Almost 99% of reciprocal trust relations established by  vertexes (each of them has far more than 250 earned merits) of that polyhedron which is DT part  circulating   in the trust system. Coincidence?

Ah shit, I broke the cursed heptagon, forgot to trust gmaxwell. Sorry about that.

[LoyceV]

Almost 99% of reciprocal trust relations established by  vertexes (each of them has far more than 250 earned merits) of that polyhedron which is DT part  circulating   in the trust system. Coincidence?

You're going to have to explain how you got to "almost 99%". From those 9 users, I have only 4 on my Trust list:

LoyceV Trusts:
2. gmaxwell (970 Merit earned) (Trust feedback) (Trust list) (BPIP)
3. Vod (984 Merit earned) (Trust feedback) (Trust list) (BPIP)
13. suchmoon (1602 Merit earned) (Trust feedback) (Trust list) (BPIP)
15. The Pharmacist (1460 Merit earned) (Trust feedback) (Trust list) (BPIP)

I’m creating an algorithm to find all the subgraphs, but it’s not complete yet.
~
I took this on as a personal challenge

Once you figured it out, will you share your algorithm? I can't think of a good way to do this.

[DdmrDdmr]

<…>

<…> The chart is not really "correct" there: What I’m, looking for are all (or at least the greatest) subgraphs that connect all to all of it’s component nodes bidirectionally (i.e. where each vertex represents that A trusts B and vice-versa, meaning that all nodes trust all nodes). In the chart above, @gmaxwell and @suchmoon are clearly not in that situation with the rest.

Besides, the Network charting tool, as it is, is good for representing unidirectional vertices, but not bidirectional vertex with the data as I have it represented there. Perhaps if I were to create another representation, with a database that loaded only bidirectional vertex it would lead to a clearer representation (I may look into it later on). What the above char is showing are only unidirectional vertex representations currently (my char was “correct” only because I checked that all those relations I marked as bidirectional were so).

-> Something like this would be better: https://www.google.com/fusiontables/DataSource?docid=18y8mSJwCj7jWpaVGZoVFyXE4WpSPaaQQTJr_3Uf0
-> All vertices are bidirectional (A trusts B and B trusts A).
-> Hover over a node to get a clearer view of the vertices.
-> Since the filter already has 5 different names added to it, to work on another different set you need to reset the filter by deleting it (with the cross) and adding it back on from the filter dropdown.
-> Enter a number of nodes greater than the max nodes (top left of chart) to see all nodes.

Full reciprocal bidirectional relationships (the larger the node, the more reciprocal relationships):

<…> Once you figured it out, will you share your algorithm? I can't think of a good way to do this.

If I manage to succeed..., which I'm now rather doubtful.  I’ve only got partial results so far and fear I’m missing out combinations. I’ll keep on it when I can get some linear time to do so. Not sure if this is going to be an np-complete kind of problem …

Edit: I've tried a different alternative which looks good, based on native SQL Server node and vertex treatment. So far I've derived all complete subgraph (all trust all) for up to 6 nodes, deduplicating paths too (with unpivot and cursors...).

Just for test purposes, the complete (all trust all) largest subgraphs I’ve managed to detect with you as a node are:
@Actmyname, @DarkStar_, @hilariousandco, @LoyceV, @suchmoon (charted in the above link)
@Actmyname, @hilariousandco, @LoyceV, @suchmoon, @The Pharmacist
Edit: found one more: @hilariousandco, @LoyceV, @marlboroza, @suchmoon, @The Pharmacist

I feel so out of it. I don't think I am in any trust or merit circles.<…>

Found this small all trust all "trust circle": @Jet Cash, @TMAN, @The Pharmacist, @Vod. My algorithm skipped it, but changing parameters it eventually detected it (which means it's not working too well yet).


These are all the 6 node complete subgraphs (all trust all)- derived with the new algoritm approach:

Code:

Funny , gysca , leancuisine , Operatr , P4ndoraBox7 , tennozer
CanadaBits , Funny , gysca , Operatr , P4ndoraBox7 , tennozer
CanadaBits , Funny , leancuisine , Operatr , tennozer , vCardVideo
CanadaBits , leancuisine , Operatr , P4ndoraBox7 , tennozer , vCardVideo
CanadaBits , Funny , leancuisine , P4ndoraBox7 , tennozer , vCardVideo
CanadaBits , Funny , gysca , leancuisine , Operatr , tennozer
devidLeench , natka , pisston , ssuchy , swetka , taktik
CanadaBits , gysca , leancuisine , Operatr , P4ndoraBox7 , tennozer
CanadaBits , Funny , gysca , leancuisine , Operatr , P4ndoraBox7
CanadaBits , Funny , leancuisine , Operatr , P4ndoraBox7 , tennozer
Bazinga442 , Deena , DutchFinity , endlasuresh , gwsukabokepjepang , Thule
CanadaBits , Funny , gysca , leancuisine , P4ndoraBox7 , tennozer
Funny , leancuisine , Operatr , P4ndoraBox7 , tennozer , vCardVideo
marlboroza , owlcatz , qwk , suchmoon , The Pharmacist , xtraelv
CanadaBits , Funny , Operatr , P4ndoraBox7 , tennozer , vCardVideo
CanadaBits , Funny , leancuisine , Operatr , P4ndoraBox7 , vCardVideo

Note that some are really subsets of a 7 node subgraph.

[DdmrDdmr]

<…> I would be curious to see any patterns of trust circles in which a group of people all trust each other.

I think I may have found all the combinations of positive trust, where by all members in a graph all trust each other.

What I’ve found are:
-   7 members where all trust all: 2 cases (complete graph networks)
-   6 members where all trust all: 16 cases (complete graph networks)
-   5 members where all trust all: 91 cases(complete graph networks)
-   4 members where all trust all: 307 cases(complete graph networks)
-   3 members where all trust all: 647 cases(complete graph networks)
-   2 members where all trust all: 3.770 cases(complete graph networks)
(note: graphs from one level have subgraphs on the levels beneath).

I’ve listed them in the last tab ("All trust All") of the link to all the data:
https://docs.google.com/spreadsheets/d/1oI11POXylBm6UqjFeb9JOkxXp2XkN4s9yMKp8To6nrQ/edit?usp=sharing

<...> Once you figured it out, will you share your algorithm? I can't think of a good way to do this.

Tell me if you want me to describe the process, but what I’ve now used is rather SQL Server based, using commands such as:

Code:

SELECT  row_number() over (order by N1.Username, N2.Username, N3.Username, N4.Username, N5.Username, N6.Username) groupId,  
		N1.Username Username1, N2.Username Username2, N3.Username Username3, N4.Username Username4, N5.Username Username5, N6.Username Username6
into tmp_6nodes
FROM	ReciprocalTrustNodes N1, ReciprocalTrustNodes N2, ReciprocalTrustNodes N3, ReciprocalTrustNodes N4,ReciprocalTrustNodes N5, ReciprocalTrustNodes N6, 
		ReciprocalTrustEdges E1, ReciprocalTrustEdges E2, ReciprocalTrustEdges E3, ReciprocalTrustEdges E4, ReciprocalTrustEdges E5, 
		ReciprocalTrustEdges E6,  ReciprocalTrustEdges E7,  ReciprocalTrustEdges E8,  ReciprocalTrustEdges E9, ReciprocalTrustEdges E10,
		ReciprocalTrustEdges E11,  ReciprocalTrustEdges E12,  ReciprocalTrustEdges E13,  ReciprocalTrustEdges E14, ReciprocalTrustEdges E15
WHERE MATCH(N1-(E1)->N2) and MATCH(N2-(E2)->N3) and MATCH(N3-(E3)->N4) and MATCH(N4-(E4)->N5) and MATCH(N5-(E5)->N6) and MATCH(N6-(E6)->N1) 
  and MATCH(N1-(E7)->N5) and MATCH(N1-(E8)->N4) and MATCH(N1-(E9)->N3) and MATCH(N6-(E10)->N4) and MATCH(N6-(E11)->N3) and MATCH(N6-(E12)->N2)
  and MATCH(N5-(E13)->N2) and MATCH(N5-(E14)->N3) and MATCH(N4-(E15)->N2) 

<+ cleansing duplicate cases>

(never used it before, and its does have its limits, but it seems interesting).