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The Outer Rim of the Global Tree

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Surnames/tags: 100_circles connection_finder connectors
Profile managers: Eva Ekeblad private message [send private message], Oliver Stegen private message [send private message], Bernard Vatant private message [send private message], and Susan Stopford private message [send private message]
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Contents

Introduction

Where is the periphery? Where is the center?

Such bold questions might seem intractable given the sheer size and everchanging, evergrowing shape of our Single Tree. One could tentatively try the famous "center is everywhere, periphery nowhere", but this simple answer works only for infinite spaces. The Single Tree is very large indeed, but finite. And it's well known that very large numbers are in fact more tricky to grasp than infinite. The tree metaphor does not scale to such "astronomical" figures. Actually the Single Tree does not look like a tree at all. A Galaxy, with its size and shape defying our imagination, seems a better metaphor.

In the framework of the 100 Circles research, we are monitoring the furthest circles of our reference profiles, the most far-flung - or eccentric - branches, extending to the Outer Rim of our Galaxy to answer the above questions.

This page provides:

  • A current table of the most eccentric profiles we have found, regularly updated.
  • A history of recent changes, branches which have recently appeared, and previous ones which have been pulled back to the center by reconnection events.
  • A presentation of methods used to identify both the eccentric profiles and elusive "central profiles".

This work has the objective to both augment our understanding of the WikiTree graph geometry, and provide a basis for action, specifically to:

  • Answer questions about the distances computed by the Connection Finder, such as : How far can two profiles be from each other? When and where are distant profiles found? Why are they so distant? Can we find the central profiles?
  • Provide the Connectors Project with another field of action. Even if Outer Rim branches are connected, their connection paths to the center of the tree are long, winding, and in many points uncertain or dubious. They are just waiting for someone to look closely at them and find new connection paths which will pull them back towards the center of the tree, strenghtening the global connection.

Current status

Updated : 2024, Apr 1st

The following table lists profiles at the tip of each current Outer Rim branch. This table is of course non exhaustive and bound to frequent changes. See last section for more explanations on how those profiles are discovered, and other mathematical details.

d country epoch profile createdupdatedPM or creatornotes
87Pakistan1900sKhurshid Anwar Hamdani Nov 2020 Jan 2021 Ali Imran Zaidi
75Belgium1800sFrançois Auguste Galet Jan 2024 Jan 2024Pierre Frappé
74Denmark1800sJens Christian JensenAug 2023Aug 2023L. Christiansen
73USA1800sWilliam Johnson Apr 2023 Aug 2023 Kate (Gardner) Schmidt
72Ireland1100sGilla na Naem mac Cú Ulad Jul 2023 Jul 2023 Richard Devlin
72Cabo Verde1800sMaria Antónia Silva Évora Oct 2023 Oct 2023 Anonymous Anonymous
71Likely EgyptLikely 1500sكريم الدين الكريمي الخالدي Dec 2011 Dec 2011Khali-7 (closed account)
71USA1900sWalter HallJan 2022Jan 2022 Nanette (Gahn) Pezzutti USBH
70USA1800sHoward SmithAug 2023Aug 2023 Kate (Gardner) Schmidt
68Italy1700sGiuseppe Derosa Jan 2023 Feb 2023 Melanie (Green) Armstrong
68Germany1800sWilhelm PlünschAug 2022Jan 2023Oliver Stegen
68Belgium1700sPetrus CuypersDec 2016Dec 2016Davy Van Eynde
68Italy1800sRocco FarielloJul 2023Jul 2023 Morgana Patrocinio Costa
67Italy1800sDomenico Fuga Dec 2017 Aug 2018 Jocenei Scremin
67China00sXiu LiuJun 2018Jul 2018 Darrell Parker
67France1700sÉtienne François Godin Feb 2023 Feb 2023 Jared Kish
67Austria1800sFranz WaldbauerSep 2020 Sep 2020 Martin Postlmayr Possible connection: Michael Gebetsberger, needs connection back to existing Austrian family in chain.
66Spain1700sJuan UrrutiaOct 2023Oct 2023 Aitor Pipaon12 profiles in same branch all at d=66, 2GGPs of Felipe Bilbao
65Germany1700sJosephus OttJun 2021Jun 2021 Peter Pfister Sr.
65Austria1700sMaria (Riedl) OberreitherDec 2020 Dec 2020 Jochen Oberreiter Notes: Has common connection to chain of Franz Waldbauer (above) through Mathias Postlmayr
65Bohemia1800sVáclav KunešFeb 2013 Feb 2013 Martin Novotný
64Austria1800sAntoni Granda (abt.1850-)Feb 2019 Jun 2019 Arndt-168 (closed account) Multiple people in path with last name of Granda in the same location / time. If a close relationship can be established between Granda-40 and Granda-50 (are they siblings?), then that would massively reduce the chain. See also possible connection to Granda-77 to reduce the chain.
63Italy1700sAntonio MarcantonioNov 2022 Nov 2022 Morgana Patrocinio Costa
63Spain1600sMartín Latorre Nov 2019 Nov 2019 Santi Díaz de Argandoña
62Spain (Pays Basque)1500sAna Zuloaga Dec 2015 Dec 2015 Fernando Agulló de Rueda
61Russia (?)1700sФедор СиличJun 2022 Jun 2022 Katia Syrayezhkina

Recent updates : In this list, "reconnected" means that a new and shorter connection path has been found, pulling the profile branch closer to the central profiles.

The reference profile : from Mary Stuart to QEII

Where is the center, and where is the periphery of the Single Tree? Is it even possible to agree on a definition of those terms, in this everchanging evergrowing network of tens of millions of nodes? Barely. Graph theory provides a wealth of possible definitions of centrality in a graph, but the underlying algorithms just do not scale to a graph of such a size.

After a lot of exchange and discussions, we have come to a pragmatic approach. The key tool is of course the Connection Finder, and the so-called "magic" query specially developed by Aleš Trtnik for the project. This query yields, for any reference profile, the distribution of distances to, and the list of profiles furthest from, this reference. A "triangulation method" has been developed which allows us to identify the most eccentric profiles, then profiles more or less equidistant from those extremes, give or take a few degrees. More mathematical details are provided at the bottom of the page, here and there.

When we began the Outer Rim study at the end of 2020, we selected Mary (Stewart) Stuart Queen of Scots (1542-1587) as a reference profile for the center of the Single Tree, mainly because the distance from her to all the "Lords of the Rim" was mostly in the 60-80 range. Despite the many changes we've seen in the Outer Rim since we started our study (see The Outer Rim archives), Mary Stuart appeared to maintain her central position, with the total number of profiles at distances over 60 hovering about 7,000. This number has fluctuated in the intervening period, at times chaotically. In Nov 2021, it rose to over 9,000. However, it subsequently dropped significantly and since March 2022, has been at its lowest observed value, around 1,400, with less than 100 profiles at distances over 65.

Why did we change our reference profile to Queen Elizabeth II? Of course her recent death put her into focus. But there were other reasons too. In April 2022, we chose QEII as the reference profile on the 100 Circles page. In July, Wikitree introduced the CC7 feature and Connection Count History which also feature QEII (and Kevin Bacon). It was therefore consistent to use her also as a reference profile for the Outer Rim.

One could wonder if QEII is "less central" than her ancestor Mary Stuart. Actually, comparing the distances of current Outer Rim profiles from Mary Stuart and from QEII have shown very small differences, less than 3 steps for most of them. Notable exceptions are the two outliers at the top at the table, who are 8 steps further from QEII than from Mary Stuart.

Why are those profiles so far away?

There are many ways for a branch of the Single Tree to expand arbitrarily far from the center, but a major process is the connection of large, previously unconnected branches. An unconnected branch might develop to gather hundreds, in rare cases thousands of profiles, typically in countries not yet much represented in WikiTree : Eastern Europe, Arabic world, Asia, Hispanic countries ... often by WikiTreers from those countries not easily communicating with the bulk community, for obvious cultural and linguistic reasons.

When such a branch is eventually reconnected to the Tree, either by its serendipitous extension or by the hard voluntary work of Connectors, it's often through a bottleneck of "bridge profiles" themselves often sitting already quite far from the center. This process can build up several times. The distance distribution for such reconnected branches will show typical bottlenecks.

The Hamdani branch is of a different kind, being connected through a very long and thin paternal line tracing back to the foundation of Islam.

The most ancient profiles in WikiTree, in the 1st century (we have no BC profiles), are likely to belong to the Outer Rim as seen from QEII. They were found at distances of Mary Stuart below 60, but not far from the limit for some of them. They are of course further from QEII, that's why Xiu Liu now appears in the table. Those very ancient profiles are unlikely to be brought much closer, since 20 centuries spans about 60 generations.

How is the Outer Rim changing?

While keeping mostly at similar distances from the center, the Outer Rim keeps changing. New branches are appearing, while other ones are pulled back to the center when new connections are made. Before we started this work, the process was happening without anyone being aware of it. Systematic monitoring is giving the opportunity to alert Connectors when a branch is starting to wander off, or when a major connection happens at far distances. When new branches appear in countries with a lot of active WikiTreers, they generally don't stay there a long time, additional connections are generally found in a matter of days, sometimes a few hours after the alert is published on G2G. Branches which have been there for years, with no more active managers, and/or created in the dark ages of wild GEDCOM imports, have not yet met WikiTreers both able and willing to work on them, and are likely to stay there for a while.

The Outer Rim population (arbitrary limit being a distance over 60 from QEII) has chaotic fluctuations, but remains a very small (even smaller and smaller in proportion) part of the total population of the Big Tree, which during the same period has grown from about 22 million to 31 million. The following table compares the number of profiles at distance over 60, and over 70 from QEII at six months intervals.

May 2021 Nov 2021 May 2022 Nov 2022 May 2023 Dec 2023
over 60 5441 8210 1323 1186 2626 4174
over 70 818 1370 30 37 251 339

Distance, eccentricity, diameter, radius, and central nodes

Note : the figures in the following sections are given as examples, they are not regularly updated with the current most distant profiles.

Definitions and basic rules

  • The graph we consider (Single Tree, Big Tree ...) is connected, which means there is at least a connection path between any two nodes (Wikitree profiles).
  • Distance between two nodes X and Y is the length of a shortest path between X and Y, or the number of "steps" needed to go from X to Y. In a graph the size of WikiTree, there are generally many such shortest paths. The Connection Finder is displaying only one of them, and gives the distance in "degrees", which is another word for "steps".
  • Eccentricity of a node X is the greatest distance from X to any other node in the graph. Example : the current eccentricity of QEII is 87, her distance from Hamdani-3.
  • The maximum eccentricity is called the diameter of the graph. The current diameter of the Single Tree is 142.
  • The minimum eccentricity is called the radius of the graph. The current radius of the Single Tree is between 71 and 73.
  • A central node is a node of minimal eccentricity. In other words, the eccentricity of a central node is equal to the radius of the graph. The following section shows how to find "quasi-central" nodes.

Some quite obvious but useful consequences of those definitions :

  • Any distance between two nodes is smaller or equal to the diameter. Put it otherwise, the diameter cannot be smaller than any arbitrary "great" distance found. For example If two nodes are found at distance 142, the diameter is at least 142.
  • Any node eccentricity is greater or equal to the radius. Put it otherwise, the radius cannot be greater than any eccentricity found. For example if a node is found of eccentricity 73, the radius cannot be greater than 73.
  • The diameter cannot be greater than twice the radius. This is a simple consequence of the triangle inequality. For example if there is a node of eccentricity 73, the diameter is at most 146.

Finding the radius and central nodes

To find central nodes in a graph the size of the Single Tree, over 27 million profiles in the current state of affairs, cannot be done by brute force (computing all distances is a non-starter). Moreover, the graph is growing by thousands of nodes a day, and the central nodes of today might not be the same as those of tomorrow. Fortunately, the simple results presented in the introduction allow a quick-and-dirty method to assess the diameter, the radius, and to find "quasi-central" nodes, with a precision good enough for the task at hand, to give an idea of the global geometry. The "magic query" used in the 100 Circles project not only provides the distribution of distances, but also yields the identity of the furthest profiles.

The method is the following (updated 25 Jan 2023)

  • Apply the query to our reference profile Windsor-1 : one of the furthest profiles from her, at distance 87 is Hamdani-3.
  • Apply the query again to Hamdani-3. The furthest profile is Kuneš-3 at distance 142, hence the diameter is no smaller than 142, and the radius is not smaller than 71.
  • Look up, using the Connection Finder the shortest path from Hamdani-3 to Kuneš-3. The middle profile is William de Warenne .
  • Applying the query to William de Warenne we find an eccentricity of 74, hence the radius is not greater than 74.
  • Looking around the middle of the path, we find Joan (Plantagenet) de Mowbray with a slightly smaller eccentricity at 73. We can conclude that the current radius is somewhere between 71 and 73.

Whenever either Hamdani-3 or Kuneš-3 is reconnected closer, or a new Lord of the Rim appears, things are bound to change.

Eccentricity vs mean distance

We monitor in the 100 Circles project some profiles with a steep growth of circles, and a very low mean distance, such as Samuel Lothrop. One could wonder if such profiles are not "more central" than the above. In a sense, they are, depending on the definition of centrality chosen. Mean distance and eccentricity are largely independent variables. Profiles with minimum eccentricity are not the ones with minimum mean distance, as the examples below illustrate.

The mean distance is far less sensitive to Outer Rim changes than the eccentricity, because it is computed over all 27 million profiles. A single change in the Outer Rim can drastically impact the eccentricity for all profiles, but will barely change the mean distance of most profiles.

History

This long section has been moved to a dedicated archives page : The Outer Rim archives





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