Connection Facts and Figures

Profile manager: Bernard Vatant [send private message]

We are all connected.

But what does "connected" mean? And who are "We"? And how are we connected?

Vocabulary

• Connection between profiles uses the family relationships: parent, child, sibling, spouse. Two profiles are said connected (to each other) if there is at least one path in WikiTree linking those two profiles, using a sequence of the above said relationships. The Connection Finder application allows to easily find out if, and how, two profiles are connected. Example : Mary Stuart and Barack Obama are connected.
• The length of a shortest path, as indicated by the Connection Finder, is called the distance between the two profiles. This distance is measured in "degrees" or "steps". Mary Stuart and Barack Obama are at distance 20 from each other, in the current state of affairs (Jan 2022 - down to 19 in July 2023)
• Two profiles being "connected" does not mean they are "relatives" or "related" in the common meaning of the term (ancestors, descendants, cousins, collaterals ...), unless under a very extensive definition of the notion of family. Which is, actually, the philosophy of WikiTree.
• The "Big Tree" or "Main Tree" or "Single Tree" or even simply "The Tree" is gathering about 85% of profiles, about to pass the 32 million milestone in Januay 2024 (30 million by July 2023). All profiles in the Big Tree are connected to each other. The usual WikiTree jargon is using "connected" and "unconnected" in an absolute way to indicate if a profile belongs or not to the Big Tree. The number of connected profiles is given by the Connection Finder page, updated daily.
• A profile connected to no other one is said "unlinked". Otherwise it is sometimes called "linked" or "related", both terms potentially confusing.
• An "unconnected branch" is a set of profiles all connected to each other, but not to the Big Tree. An unlinked profile is under this definition, technically an unconnected branch of size 1, although calling this a branch might seem strange.

This vocabulary is not globally consistent, and people don't always use it in a consistent way, and it's easy to be confused when the context is unclear. For example "an unconnected branch is composed of unconnected profiles, all connected to each other", sounds weird until you grasp that "unconnected" is taken with an absolute meaning, whereas "connected" is relative (to each other).

Many small unconnected branches

How many distinct unconnected branches there are outside the Big Tree is not obvious to assess. Looking up the Unconnected People pages tends to indicate that most unconnected branches are very small, like ten members or less.

Thanks to data provided by Aleš Trtnik on the total number of branches and their distribution by size, we got a confirmation of this first impression. The following table is a summary of this distribution, data as of January 2022, updated in January 2024.

The evolution shows a diminution of 20% for the number of large unconnected branches (size over 50). Those are listed and in the radar of Connectors. But on the other hand the number of very small branches (size up to 5) has grown by about 30%.

The following plots gives the number distribution for branches of sizes from 2 to 20 in January 2022. It shows clearly the exponential decay of the number of branches. The distribution as of January 2024 is similar.

Number of unconnected branches by size

Details of the "long tail" of largest unconnected branches are found in the Largest Unconnected Branches page. As of January 2024, the largest branch counts over 5,000 profiles, and there are 18 branches of size over 1,000.

No large branch outside the Big Tree

No unconnected branch has more than a few thousands members. Even the most "exotic" and largest ones are smaller than the Big Tree by at least 3 orders of magnitude.

Why is it so? Let's try two kinds of explanation.

First obvious explanation is Connectors! Large unconnected branches are in their radar of course, and they work hard, 24/24 and 365/365, to connect them to the Big Tree. They are of course all the more efficient than the countries of unconnected profiles are already well represented in WikiTree, the sources easily available etc. It explains why most largest branches belong to regions of space and/or time a bit distant from the (Western Anglo-Saxon) bulk of the Big Tree, making them more difficult to connect.

The other possible explanation calls probability computation, and is more arguable, but let's try it nevertheless.

The total number of humans likely to ever have a profile in WikiTree - that is whoever has been named and documented in at least one reliable source - is difficult to assess. Most people who lived before the recent centuries have never been documented. The possible number of potential profiles could be anywhere in the 10 to 50 billions range, growing by tens of millions of births yearly. For the present computation, let's take a conservative upper value of 25 billions.

The current size of the Big Tree, 25 millions, is roughly one thousandth of the above. Otherwise said, if you pick a random documented human X, the probability for X to have a profile in WikiTree is about 0.001, assuming that the Big Tree is somehow a big random sample of all potential profiles. Otherwise said, the probability of X to fall outside the Big Tree is 0.999.

Now take a random branch of n profiles. The probability that no profile in this branch fall in the Big Tree is about 0.999^n. Let's compute it for different values of n.

• 0.999^100 = 0.90
• 0.999^1000 = 0.37
• 0.999^5000 = 0.01
• 0.999^10000 = 0.000045

A random branch of 100 members has only 10% chance to be connected, the probabilty is 63% for 1,000 members, 99% for 5,000 ... and practically 1 (certainty) for n over 10,000.

Branches are not random samples of documented humans, but the more they grow, the more they expand in all directions and the closer to random they become. Samely, the Big Tree is not a random sample of all potential profiles, but the more it grows, the more random it becomes. Nevertheless, despite all its biases, this simple model agrees in its main conclusion with the observed data : unconnected branches size is very unlikely to pass the thousands threshold.

Time distribution of connected and unconnected profiles

The following plot shows the breakdown of connected and unconnected profiles by ten-year period, as provided by the WikiTree+ application (data January 2024).

Breakdown of connected profiles by ten-year periods

Several remarks about this plot

• Each profile is counted in every period the person has been found living, based on presence of birth and death date.
• It is based on WikiTree+, so it excludes Living and Private profiles, which explains the low numbers of profiles post-1950, either connected or not.
• Despite this bias, the best connected period is around 1800, where almost 95% of profiles are connected.

Breakdown of connected profiles by ten-year periods

Distances in the Big Tree : closer and closer

The 100 Circles and related pages are discussing in details the distribution of distances in the Big Tree, aka "population of circles" for various reference profiles. We list here the main points to bring home.

• Central profiles of the Big Tree have a typical mean distance of 20 degrees to other profiles, with 95% at distance lower than 30. The long tail of far-flung branches, extending typically at distances from 40 to 80, is representing less than 1% of profiles.
• The average distance between two random connected profiles, based on samples constructed using Jamie Nelson's very cool application, can be assessed, as of Aug 2022, to be in the interval [24,27] with a confidence of about 95%. See G2G discussion for more details.
• The mean distance is slowly but steadily getting smaller for all studied reference profiles. The peak of the distance distribution is getting sharper and shifted to lower values. The following table shows the changes in mean distance for a few reference profiles we've been following in the framework of the 100 Circles project.

Could this trend keep on going? There are still a lot of missing relatives everywhere in the Big Tree, and more reconnections will happen, and distances are likely to keep getting smaller in the near future.

There are of course limits to the collapse of distances and completion of circles. In the page Ten circles meet each other, based on the case study of Samuel Lothrop, we conjecture that in the long run, most profiles in the Big Tree could be less than 20 steps from each other.

All streams flow to the sea

For all of us connectors, the main practical lesson to bring home from the above facts and figures could be the famous quote of a great martial artist. Be like water, my friend.

Don't waste your energy banging your head on a brick wall when so many side paths are open, waiting for you to pass by without efforts. Don't fight an impossible way uphill when the flow is inviting you downhill or sideways. If you don't find the father, follow the sister and her in-laws to wherever they want to lead you.

Like water, follow the flow through all open serendipitous paths, let connection streams find their way through any obscure narrow ravines, let them meander in unknown valleys. As long as they flow, at some point they'll reach the ocean of the Big Tree.

Like water, move gently outwards and around, in all possible directions, leading you beyond your current projects, categories, countries, families, names, languages ... all things likely to close your eyes and mind to possible paths. Don't be afraid of following the outliers, the renegades, the migrants, the illegitimate, the runaways, all likely to be the best of connectors.

Forget where you're bound to go, the path will lead you there. And enjoy each step.