Recent work has proven the existence of extreme inbreeding in a European ancestry sample taken from the contemporary UK population nature_01. This result brings our attention again to a math problem related to inbreeding family trees and diversity. Groups with a finite number of individuals could give a variety of genetic relationships. In the present work, we present this key question: given a particular number of ancestors at each generation, how many different hypothetical trees can be constructed? Building upon our previous works, we propose an approach to estimate this number. Given that this number is quite large, we also address the non-trivial issue of tree representation . We present an open-source python code to generate the tree graph and the adjacency matrix  for each different tree representation. We show how this mapping reflects the diversity in the different tree representations , and how valuable information may be extracted upon inspection of these matrices. The  code presented here, available in Git-Hub, may be easily modified to be applied to other areas of interest involving connections between individuals, such as models of opinion spread .
Recent work has proven the existence of extreme inbreeding in a European ancestry sample taken from the contemporary UK population nature_01. This result brings our attention again to a math problem related to inbreeding family trees and diversity. Groups with a finite number of individuals could give a variety of genetic relationships. In previous works \mbox{%DIFAUXCMD PhysRevE.92.052132, PhysRevE.90.022125, JARNE20191 . We present an open-source python code to generate the tree graph , the adjacency matrix , and the histogram of the links for each different tree representation. We show how this mapping reflects the difference between tree realizations , and how valuable information may be extracted upon inspection of these matrices. The algorithm includes a feature to average several tree realizations, obtain the connectivity distribution, and calculate the average and mean value. We used this feature to compare trees with a different number of generations and nodes. The code presented here, available in Git-Hub, may be easily modified to be applied to other areas of interest involving connections between individuals, extend the study to add more characteristics of the different nodes, etc .
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In the present work, we present this key question: given a particular number of ancestors at each generation, how many different hypothetical trees can be constructed? Building upon our previous works, we propose an approach to estimate this number. Given that this number is quite large, we also address the non-trivial issue of tree representation
In previous works \mbox{%DIFAUXCMD PhysRevE.92.052132, PhysRevE.90.022125, JARNE20191
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and
,
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, and the histogram of the links
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diversity in the different tree representations
difference between tree realizations
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algorithm includes a feature to average several tree realizations, obtain the connectivity distribution, and calculate the average and mean value. We used this feature to compare trees with a different number of generations and nodes. The
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such as models of opinion spread
extend the study to add more characteristics of the different nodes, etc