Have you checked the WikiTree+ function to find cycles?

Question

Following a previous post about cycles, Aleš has developed a function on WikiTree+, leveraging the Connection Finder.

The URI of the function is : https://plus.wikitree.com/default.htm?report=disp3

The function takes as input two profile IDs, ID1 and ID2. The path from ID1 to ID2 must contain at least 3 profiles (in other words distance of ID1 to ID2 is at least 2 steps).

To get familiar with the function, start with a simple path of length 3, e.g., ID1 = your mother and ID2 = your paternal grandfather (assuming your parents are linked by a "spouse" relationship) ...

... more about it here : https://www.wikitree.com/wiki/Space:Cycles_and_Holes_in_the_Big_Tree#Finding_cycles_with_WikiTree.2B

Comments

Oof, I'm pretty good with math, but haven't studied graph theory. Some of the names here (geodesic cycles, endogamic clusters) take some reading.

Regarding the over-simplification of calling it the "big tree" or "global tree", I think we need to emphasize it looks like a banyan tree, or maybe a mangrove forest. Not your typical oak or elm!

Banyan tree: 

---

Sure! In the previous conversation I mentioned this image : https://futuretreehealth.com.au/wp-content/uploads/2023/03/hollow-tree.jpg

If you have that kind of image free of copyright I would gladly add it to the FSP!

---

Rob's is at

https://commons.wikimedia.org/wiki/File:Banyan_tree_Cleveland.jpg

Also see

https://commons.wikimedia.org/wiki/File:Banyan_Tree_at_The_Valley_School_,_Bangalore.JPG

---

George, this is a separate announcement for a WikiTree+ function developed in the framework of a previous conversation at https://www.wikitree.com/g2g/1685340/cycles-and-holes-in-the-big-tree

There is a full Free Space Page I have taken time to develop with examples. It's not an obvious topic and needs a bit of homework if you sincerely want to answer your questions. Please take the time to read it thoroughly ... or to ignore it altogether if your only interest in WikiTree is finding your ancestors and close cousins.

https://www.wikitree.com/wiki/Space:Cycles_and_Holes_in_the_Big_Tree

---

Thx Jim! If the image if in Wikiemedia Commons, we can use it for the page. Great!

Answer 1

Thanks, Bernard et al. I've recently had fun decreasing the cycles between some of my US ancestors. This will really help focus on reducing the cycles I have with my family in the UK. I appreciate all your hard work.

Susie :-)

Answer 2

This looks like fun. I'm not sure yet what it's useful for.

I tried a couple of pairs, at the top of one is "This cycle is not geodesic" and the other "This cycle is geodesic" (only the second has the word in bold). There is no footnote or hyperlink to explain either the definition of geodesic nor the significance of why it matters that some cycles are geodesic and others aren't.

Could those explanations be added somewhere obvious please?

Comments

Thx Scott for the feedback. Is it useful? We are in early stages of research, all that is quite fresh, and like any open research, you never know what you'll find out. Otherwise it's call engineering :-) Will it be useful? Time will tell.

Geodesic cycles are defined here : https://www.wikitree.com/wiki/Space:Cycles_and_Holes_in_the_Big_Tree#Geodesic_paths_and_geodesic_cycles

Aleš is waiting for the documentation on this section to be stable in order to copy it in the WikiTree+ doc. See the previous post for further conversation on this. 

A large geodesic cycle (say, length over 30) indicates that the graph is "sparse" in this region, and shortcuts are probably to be discovered. It's in the same spirit as discovering the "Outer Rim" branches, putting light on places where more new connections are needed.

On the other hand, presence of small cycles (length around 10) is an indication of local endogamy, often in a dense part of the graph. Of course wherever the final documentation sits, it would be good to have linked from the function report, you're right.

---

Predicting shortcuts is a tricky business, but one option might be looking for parents with only one child. In most cases, this is probably because somebody was working from their generation upward. Filling in the parents, but not bothering to fill in all the siblings of each family. (I know I've done this at times).

---

My non-geodesic example arose from a profile I had just created before reading this post. I created one new profile and connected it to both her daughter and her mother - the two profiles I entered to this tool. The short path between these is the new path of length two. The long way round the loop is the 17 degrees before I added the new profile. The outcome is a non-geodesic cycle of length 19.

The antipodal distances are shown like
0 to 9: 8
0 to 10: 9
One of 8 and one of 9 except at the far end of the cycle I get
10 to 0: 9
10 to 1: 9
and
11 to 1: 9
11 to 2: 9

In case it matters - Date of report: 2024-01-14 00:38:14 Date of Data: 7 Jan 2024

The new profile was Larwood-186 created on 11 Jan 2024 so is this just an oddity of using current distance data and old cycle data or something? Will it "become geodesic" when the offline database is updated?

---

Scott, thanks for following up. Looking now at your example I'm trying to figure what is happening. Thinking aloud here, so apologies is some of the following are already obvious to you.

If I get you correctly, the path you are speaking about is : https://plus.wikitree.com/function/WTPathCycle/PathCycle.htm?WikiTreeID1=Stark-3232&WikiTreeID2=Steward-2309

First thing : the new profile Larwood-186 is not identified in the WT+ report because it's not in the WT+ dump since it was created after. See at the end of the report : Date of Data: 7 Jan 2024. This profile is by default marked as "private/unlisted" in the report, with no data. It's "node 1" in the first table, and "node 0" in the cycle.

Next week, when the dump is updated, this profile will appear in clear, with its ID, name etc, since it's an open profile.

But : this node is already known by the Connection Finder when the function calls it, since the CF is updated almost in real time. Hence the computed antipodal distances should not change when WT+ is updated (barring other changes like new profiles and/or connections which would change the local network geometry)

So, why is this cycle not geodesic, but "almost"? All antipodal distances are either 8 or 9. Since it's a odd cycle, each node has two antipodes. For each node, at least one antipodal distance is 9, for some nodes, both are 9.

This is a very frequent result, actually the most frequent, and there is a general explanation I will try to add to the documentation at some point, and hopefully what I explain here is a kind of blueprint for it.

The distance found means there is a "chord" somewhere in the cycle, that is somewhere in the path a triple (a,b,c) where a and c are at distance 1. It cannot be in the path from 1 to 18, otherwise this path would not be a shortest path in the graph minus node 0. So it's either (0,1,2) or the other way round (0,18,17). Not (18,0,1) since we know that one is of length 2.

Checking manually or with the CF : Larwood-186 (0) is at distance 2 from Morris-1608 (2) so that is not the shortcut.

But Larwood-186 is at distance 1 from Larwood-74 (17). They are siblings, and that is the responsible shortcut.

Now we know which node to strike off the path to get a geodesic cycle, it's their common mother Steward-2309 (node 18). Checking the path from Stark-3232 to Larwood-74 ...

https://plus.wikitree.com/function/WTPathCycle/PathCycle.htm?WikiTreeID1=Stark-3232&WikiTreeID2=Larwood-74

... you get as expected a geodesic even cycle of length 18.

Quod erat demonstrandum

Note that I had to refresh the page 3 times in the first example to get all the antipodal distances because of the timeout of 30s, which is not a bug but a feature, as explained by Aleš somewhere in the other conversation.

The even cycle is processed twice as fast, because you have only 9 distances to check.

---

Thank you! You did understand the path correctly.

I either knew or guessed the first parts The section from "This is a very frequent..." was new and helpful.

I'm still not clear how your worked example managed to eliminate Steward-2309 which was one of the two profiles I started from. It feels a bit like you found a different cycle than the one I was looking for. You bridged and eliminated one of the starting nodes.

As an interesting aside of playing with this tool, I found someone on the "other side" of a geodesic cycle through my marriage - he's on the 7th circle of my wife's CC7 through her grandmother and also my CC7 through my grandfather. Several edges of the cycle are marriages, so we aren't distant cousins yet.

---

Scott, I've been working on this section of the FSP : https://www.wikitree.com/wiki/Space:Cycles_and_Holes_in_the_Big_Tree#Finding_cycles_with_WikiTree.2B

In the section "Interpreting the output" I will try to explain how you derive a geodesic cycle from a "almost" geodesic one, like in your example, with illustrations ... Stay tuned!

Answer 3

I followed the discussion in the previous posting, but didn't have anything to contribute to the math or vocabulary.

In its current state I find it useful for finding cycles worth looking at - I've been bumbling around a bit, trying to find cycles in areas of Sweden I expect to be sparsely populated. I tended to go nuts because of losing orientation when working manually with the Connection Finder. This WT+ tool helps a lot with that. I didn't quite "get it" in its initial state, but after your discussions and modifications I think I do.

It's not my primary project at the moment, but I think I'll keep tinkering with it now and then.

Answer 4

Thank you for creating the help information to explain Aleš new WT+ search function. The explanation was excellent. Now that I understand how it works, how do I use the information to build a better Tree? 

Comments

Your question is like asking the astrophysician : OK now I know our universe is 13 billion years old, and holds hundreds of billions of galaxies, each with so many stars and planets. How do I use this knowledge to make this planet a better world?

The million $ question, right? To be honest, I don't know. I don't know what is a "better Tree", to begin with. But let me try to answer anyway.

Like several previous similar attempts, the Connnection Finder itself, and all the 100 Circles affair, the primary intention of such tools is to cast light on geometry, structures, features, patterns ... of this monstruous graph which we call the Big Tree.

Large cycles, I have thought, would point (like the Outer Rim branches) towards areas where the graph is sparse, and need further research. No big deal, really, because most of us already know many such areas, and work to populate them. You do that for USBH, we Europeans do that in each of countries, regions, even villages.

The first results we get, not only from using Aleš's tool, but also parallel work of Shawn Ligocki with his independent algorithm, show that things are certainly less simple than what we had thought.

Now very concretely : When you've find a quite large cycle, say in the 30-50 range, taking the round trip, checking and possibly completing the circles around each profile in the path, you might find new connections, allowing to shortcut the cycle. Any new such connection will get us closer. Which is, seems to me, a way to get a better Tree.

As Debi Hoag wrote in another conversation, a large cycle is a hole in the Tree, take it as yet another rabbit hole.

---

"When you've find a quite large cycle, say in the 30-50 range, taking the round trip, checking and possibly completing the circles around each profile in the path, you might find new connections, allowing to shortcut the cycle."

This is very helpful. It helps us find possible new connection points so we can tighten the web. 

---

That's the idea, exactly. Time will tell if it's efficient or not ...

Answer 5

Bernard, I got another idea for a report. It would start from a person and check all triplets in his nuclear family excluding the starting profile for geodesic cycle.

It could continue for CC2 and maybe CC3.

Comments

Cool. I had started to look at that manually (but using your function) for my reference profile Vatant-5, so you could test on this profile. He has a C1 of 22, but you will get mostly short cycles. His circles are very very endogamic.