The persistent homology of genealogical networks

Applied Network Science

Research

Taylor Gledhill¹  Robert Snellman¹  Raelynn Wonnacott¹  Nick Callor¹  Benjamin Webb¹  Abigail Jenkins¹  Zachary M. Boyd¹ 

[1] Department of Mathematics, Brigham Young University, 84602, Provo, UT, USA;

关键词: Persistent homology;    Genealogical networks;    Social networks;    Persistence curves;    Bottleneck distance;   

DOI  :  10.1007/s41109-023-00538-7

 received in 2022-07-13, accepted in 2023-01-27,  发布年份 2023

来源: Springer

【 摘 要 】

Genealogical networks (i.e. family trees) are of growing interest, with the largest known data sets now including well over one billion individuals. Interest in family history also supports an 8.5 billion dollar industry whose size is projected to double within 7 years [FutureWise report HC-1137]. Yet little mathematical attention has been paid to the complex network properties of genealogical networks, especially at large scales. The structure of genealogical networks is of particular interest due to the practice of forming unions, e.g. marriages, that are typically well outside one’s immediate family. In most other networks, including other social networks, no equivalent restriction exists on the distance at which relationships form. To study the effect this has on genealogical networks we use persistent homology to identify and compare the structure of 101 genealogical and 31 other social networks. Specifically, we introduce the notion of a network’s persistence curve, which encodes the network’s set of persistence intervals. We find that the persistence curves of genealogical networks have a distinct structure when compared to other social networks. This difference in structure also extends to subnetworks of genealogical and social networks suggesting that, even with incomplete data, persistent homology can be used to meaningfully analyze genealogical networks. Here we also describe how concepts from genealogical networks, such as common ancestor cycles, are represented using persistent homology. We expect that persistent homology tools will become increasingly important in genealogical exploration as popular interest in ancestry research continues to expand.

【 授权许可】

CC BY   
© The Author(s) 2023

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