Boyd Zachary M, Callor Nick, Gledhill Taylor, Jenkins Abigail, Snellman Robert, Webb Benjamin, Wonnacott Raelynn
Department of Mathematics, Brigham Young University, Provo, UT 84602 USA.
Appl Netw Sci. 2023;8(1):15. doi: 10.1007/s41109-023-00538-7. Epub 2023 Feb 23.
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.
系谱网络（即家族树）正越来越受到关注，目前已知的最大数据集包含超过十亿人。对家族历史的兴趣还支撑着一个规模达85亿美元的产业，预计其规模将在7年内翻番[FutureWise报告HC - 1137]。然而，数学界对系谱网络的复杂网络特性关注甚少，尤其是在大规模情况下。由于结成联盟（例如婚姻）的行为通常发生在直系亲属之外，系谱网络的结构特别引人关注。在大多数其他网络，包括其他社交网络中，关系形成的距离没有类似的限制。为了研究这对系谱网络的影响，我们使用持久同调理论来识别和比较101个系谱网络和31个其他社交网络的结构。具体来说，我们引入了网络持久曲线的概念，它编码了网络的持久区间集。我们发现，与其他社交网络相比，系谱网络的持久曲线具有独特的结构。这种结构差异也延伸到了系谱网络和社交网络的子网络，这表明，即使数据不完整，持久同调理论也可用于有意义地分析系谱网络。在这里，我们还描述了如何使用持久同调理论来表示系谱网络中的概念，如共同祖先循环。随着大众对族谱研究的兴趣持续增长，我们预计持久同调理论工具在族谱探索中将变得越来越重要。
