Massive Family Trees in Genealogical Research

• Massive family trees are vast genealogical networks built from user-generated records that capture kinship ties, temporal migration, and demographic history.
• Data engineering pipelines standardize and deduplicate records, enabling reliable graph construction, geocoding, and linkage across millions of individuals.
• Temporal inference and persistent homology reveal structural hallmarks like small-world behavior and heavy-tailed distributions, enriching the analysis of intergenerational migration flows.

Searching arXiv for recent and foundational papers on large-scale genealogical networks and family trees. Massive family trees are population-scale genealogical datasets in which user-generated family trees are used to construct family networks across many generations and far into the past. In this literature, the operative object is usually a genealogical network rather than a literal tree: family trees contain information on individuals such as birth and death places and years, and kinship ties, e.g., parent-child, spouse, and sibling relationships; at larger scales they are modeled as sparse graphs with parent-child edges together with union edges, and the largest known data sets now include well over one billion individuals (Koylu et al., 2020, Boyd et al., 2023). Such corpora support quantitative work on migration, demographic history, network topology, and comparative structure, including integrated analyses that combine network-theoretic structure with an inferred notion of time (Carlson et al., 16 Jun 2026).

1. Provenance, scope, and corpus composition

Massive family trees are assembled from digitised genealogical platforms and repositories with heterogeneous provenance. One line of work uses RootsWeb.com user-uploaded GEDCOM files, totaling $\approx 80$ million distinct records with name, birth/death place (text), birth/death year and kinship pointers; another uses WikiTree, a free, collaborative worldwide genealogy platform, with 6.67 million distinct individual profiles organized into several hundred thousand connected family-tree components and spanning over 160 countries; more recent comparative work uses over one hundred datasets from the Kinsources repository (Koylu et al., 2020, Fire et al., 2014, Carlson et al., 16 Jun 2026).

The geographic and temporal reach of these corpora is correspondingly broad. The WikiTree-based study reports temporal coverage c. 1 AD – present, with the bulk of reasonably complete records from 1650–1950, while the migration study extracted state-to-state migration patterns over a period of 150 years between 1776 and 1926 from cleaned, geocoded and connected family trees (Fire et al., 2014, Koylu et al., 2020). This scale is analytically consequential because it permits the extraction of migration networks over time, the testing of demographic hypotheses on fertility, lifespan, and marriage patterns, and the comparison of genealogical networks with other social networks under a common graph-theoretic and topological framework (Fire et al., 2014, Boyd et al., 2023).

A recurrent methodological premise is that these data are not typically created by trained genealogists. Accordingly, large-scale studies pair breadth with validation: aggregate lifespans were compared to published life tables with median absolute error $< 2$ years, and other analyses explicitly emphasize conflict resolution, duplicate detection, and downstream tagging of unresolved conflicts (Fire et al., 2014, Koylu et al., 2020). This suggests that “massive” refers not only to cardinality, but also to the need for reproducible pipelines for record linkage, geocoding, graph construction, and uncertainty management.

2. Data engineering, linkage, and graph construction

The computational treatment of massive family trees begins with record standardization. In the RootsWeb workflow, personal names were normalized via uppercase, strip punctuation, remove honorifics (“Jr.”, “II”), and place strings were tokenized and canonicalized; in the WikiTree workflow, names were normalized by case-folding and diacritic removal, while dates were converted to integer years and impossible dates were set to NULL (Koylu et al., 2020, Fire et al., 2014). These steps define the attribute space on which record linkage operates.

Deduplication is handled through blocking and similarity scoring. One pipeline blocks on standardized name + birth year $\pm 1$ to generate candidate pairs and computes

$$\operatorname{sim}(r_1,r_2)=w_1\cdot \operatorname{nameSim}+w_2\cdot \operatorname{placeSim}+w_3\cdot \operatorname{parentNameSim},$$

after which records with $\operatorname{sim}>\tau$ are merged and all incoming and outgoing relationships are updated to a canonical individual ID (IID) (Koylu et al., 2020). A second pipeline uses a Fellegi-Sunter–style model with feature weights for name string similarity (Jaro-Winkler), birth-year proximity, and place-of-birth match (Fire et al., 2014). When two records claim different birth years or places but pass the dedup threshold, the RootsWeb study prefers the value appearing in more independent GEDCOMs and tags unresolved conflicts for downstream analysis $(\approx 0.2\%$ of records) (Koylu et al., 2020).

Geocoding converts free-text place strings into usable coordinates. In the RootsWeb study, all unique place strings $(\approx 120\text{ K distinct tokens})$ were submitted in batch to a geocoding service, disambiguation used state or country context, edit-distance to the full string, and preference for higher-population features, and successful output was obtained for $\approx 85\%$ of unique place names (Koylu et al., 2020). Invalid coordinates were re-queried or labeled “unknown,” and pairs with no geocoded birthplace for either end were dropped in migration extraction (Koylu et al., 2020).

After linkage, the data are represented as large sparse graphs. For $N\approx 80$ M individuals and $M\approx 41.5$ M parent–child edges, the RootsWeb study stores adjacency lists and uses Compressed Sparse Row (CSR) for directed edges, key-value stores indexing $< 2$0, and memory-mapping of binary adjacency files for out-of-RAM processing (Koylu et al., 2020). A union-find structure connects linked components, with the giant component covering $< 2$1 of IIDs; records lacking parent pointers are retained but excluded from intergenerational flow counts (Koylu et al., 2020). In the more general graph model, nodes are individuals and edges are of two types: parent-child and spouse or union edges (Fire et al., 2014, Boyd et al., 2023).

3. Temporal inference and intergenerational migration

A central application of massive family trees is the reconstruction of parent-child migration flows. In the RootsWeb study, birthplaces and birthyears of parents and children are used to extract intergenerational migration flows between states, and each parent–child “move” is timestamped at

$< 2$2

For each parent–child pair with valid $< 2$3, $< 2$4 and migration year in period $< 2$5, the raw flow count is incremented as

$< 2$6

subject to the “one-count per parent-state-sex” rule, which avoids over-counting large families in migration tallies (Koylu et al., 2020).

Temporal partitioning is a major analytical choice. Three strategies were evaluated: predefined historical periods, overlapping fixed-length windows, and variable-length equal-volume windows (Koylu et al., 2020). The predefined periods are 1776–1820, 1820–1862, 1862–1890, and 1890–1926; they align with key events and are easy to interpret, but have unequal time-span lengths and unequal total moves per period (Koylu et al., 2020). Overlapping fixed-length windows provide uniform temporal granularity and sliding-window trends, but overlap complicates independence of observations (Koylu et al., 2020). Variable-length equal-volume windows give each bin comparable sample size and good statistical power, but unequal interval lengths may split known historical epochs awkwardly (Koylu et al., 2020). The accompanying best-practice advice is to test multiple schemes and report sensitivity (Koylu et al., 2020).

To control for marginal origin/destination volumes and geographic distance, raw flows are transformed using a double-constrained gravity model. Expected flows satisfy

$< 2$7

with constraints $< 2$8 and $< 2$9, where $\pm 1$0 is the great-circle distance between state centroids and $\pm 1$1 are balancing factors found via Iterative Proportional Fitting (IPF) (Koylu et al., 2020). The modularity transformation is then

$\pm 1$2

Retaining only $\pm 1$3 edges or coloring by sign highlights over-represented migration corridors and under-served or inhibited channels; the stated rationale is that subtracting the gravity-model expectation controls for “bulk” effects of population size and distance, revealing culturally or historically salient flows (Koylu et al., 2020). The preliminary result is longitudinal population mobility in the U.S. on such a large spatial and temporal scale (Koylu et al., 2020).

4. Genealogical networks, cycles, and persistent homology

A common misconception is that a family tree is structurally a tree. In the graph model used for large-scale analysis, a genealogical network is an undirected graph $\pm 1$4 with

$\pm 1$5

where union denotes marriage or any relationship that produces a child (Boyd et al., 2023). Because unions typically join individuals of roughly the same generation but at graph-distance $\pm 1$6 or $\pm 1$7, genealogical networks admit loops that do not occur in ordinary rooted-tree formalisms (Boyd et al., 2023). Common-ancestor loops, union loops, and hybrid loops are therefore intrinsic features rather than anomalies (Boyd et al., 2023).

Persistent homology provides a formal way to analyze these loops. The construction begins with graph-distance $\pm 1$8 and the distance-based filtration $\pm 1$9, where $$\operatorname{sim}(r_1,r_2)=w_1\cdot \operatorname{nameSim}+w_2\cdot \operatorname{placeSim}+w_3\cdot \operatorname{parentNameSim},$$0 has the same vertex set and an edge $$\operatorname{sim}(r_1,r_2)=w_1\cdot \operatorname{nameSim}+w_2\cdot \operatorname{placeSim}+w_3\cdot \operatorname{parentNameSim},$$1 whenever $$\operatorname{sim}(r_1,r_2)=w_1\cdot \operatorname{nameSim}+w_2\cdot \operatorname{placeSim}+w_3\cdot \operatorname{parentNameSim},$$2, so that $$\operatorname{sim}(r_1,r_2)=w_1\cdot \operatorname{nameSim}+w_2\cdot \operatorname{placeSim}+w_3\cdot \operatorname{parentNameSim},$$3 (Boyd et al., 2023). For each $$\operatorname{sim}(r_1,r_2)=w_1\cdot \operatorname{nameSim}+w_2\cdot \operatorname{placeSim}+w_3\cdot \operatorname{parentNameSim},$$4, the homology groups $$\operatorname{sim}(r_1,r_2)=w_1\cdot \operatorname{nameSim}+w_2\cdot \operatorname{placeSim}+w_3\cdot \operatorname{parentNameSim},$$5 over $$\operatorname{sim}(r_1,r_2)=w_1\cdot \operatorname{nameSim}+w_2\cdot \operatorname{placeSim}+w_3\cdot \operatorname{parentNameSim},$$6 define a persistence module, and each homology class yields a half-open interval $$\operatorname{sim}(r_1,r_2)=w_1\cdot \operatorname{nameSim}+w_2\cdot \operatorname{placeSim}+w_3\cdot \operatorname{parentNameSim},$$7 (Boyd et al., 2023). The paper introduces the persistence curve

$$\operatorname{sim}(r_1,r_2)=w_1\cdot \operatorname{nameSim}+w_2\cdot \operatorname{placeSim}+w_3\cdot \operatorname{parentNameSim},$$8

equivalently $$\operatorname{sim}(r_1,r_2)=w_1\cdot \operatorname{nameSim}+w_2\cdot \operatorname{placeSim}+w_3\cdot \operatorname{parentNameSim},$$9, as a summary that encodes how many generators persist at each scale (Boyd et al., 2023).

The interpretation of homological dimensions is explicitly genealogical. For $\operatorname{sim}>\tau$0, $\operatorname{sim}>\tau$1 drops from $\operatorname{sim}>\tau$2 at $\operatorname{sim}>\tau$3 down to the number of connected components at $\operatorname{sim}>\tau$4; each connected component is a disjoint “family group” (Boyd et al., 2023). For $\operatorname{sim}>\tau$5, each persistent 1-cycle corresponds to a nontrivial loop in the family tree, including common-ancestor loops and double-cousin-style union loops (Boyd et al., 2023). For $\operatorname{sim}>\tau$6, closed 2-surfaces are rare but can detect complex intermarriage patterns (Boyd et al., 2023). Empirically, the study computed $\operatorname{sim}>\tau$7 for 101 genealogical and 31 other social networks and found that genealogical networks have a distinct structure: $\operatorname{sim}>\tau$8 is much flatter, with significant mass out to $\operatorname{sim}>\tau$9–$(\approx 0.2\%$0 and cycles of length $(\approx 0.2\%$1–$(\approx 0.2\%$2, whereas social networks rise steeply at small $(\approx 0.2\%$3 and saturate by $(\approx 0.2\%$4 or $(\approx 0.2\%$5 (Boyd et al., 2023). The same signatures persist under subsampling, and bottleneck distances in $(\approx 0.2\%$6-diagrams group genealogical apart from social networks even with $(\approx 0.2\%$7 missing data (Boyd et al., 2023).

Scalability is addressed algorithmically rather than by exact all-pairs methods. Exact Rips-complex PH is worst-case $(\approx 0.2\%$8 and impossible for $(\approx 0.2\%$9, but the paper emphasizes sparse adjacency lists, landmark-based reduction via witness complexes, partition-and-merge via Mayer–Vietoris, and practical implementations that can handle $(\approx 120\text{ K distinct tokens})$0 nodes if restricted to $(\approx 120\text{ K distinct tokens})$1 and if edge-threshold $(\approx 120\text{ K distinct tokens})$2 (Boyd et al., 2023). A plausible implication is that topological summaries are most effective when coupled to sparsification and restricted homological dimension.

5. Structural hallmarks and inferred temporal layers

Comparative analysis across over one hundred genealogical datasets indicates that massive family trees exhibit recurrent structural regularities. Degree counts are decomposed into unions $(\approx 120\text{ K distinct tokens})$3, children $(\approx 120\text{ K distinct tokens})$4, and total degree $(\approx 120\text{ K distinct tokens})$5; empirically, for $(\approx 120\text{ K distinct tokens})$6,

$(\approx 120\text{ K distinct tokens})$7

and for $(\approx 120\text{ K distinct tokens})$8,

$(\approx 120\text{ K distinct tokens})$9

Component sizes also follow heavy-tailed laws: for 1-components, $\approx 85\%$0 with $\approx 85\%$1 for $\approx 85\%$2, and for 2-components, $\approx 85\%$3 with $\approx 85\%$4 for $\approx 85\%$5 (Carlson et al., 16 Jun 2026). The accompanying interpretation is that there is no “typical” family size or component (Carlson et al., 16 Jun 2026).

The same study reports small-world behavior with respect to both genetic and union-based distances. If $\approx 85\%$6, $\approx 85\%$7, and $\approx 85\%$8, then as the network grows $\approx 85\%$9, both $N\approx 80$0 and $N\approx 80$1 grow logarithmically in $N\approx 80$2 (Carlson et al., 16 Jun 2026). The global clustering coefficient

$N\approx 80$3

is high, with $N\approx 80$4 for the aggregate network and $N\approx 80$5 across individual datasets, reflecting the ubiquity of parent–parent–child triangles (Carlson et al., 16 Jun 2026).

A notable structural claim is that 2-components provide a natural unit of genealogical structure. A 2-component is a maximal subgraph in which every pair of vertices is joined by at least two vertex-disjoint paths, and in a union-complete genealogy every parent–child or union edge lies on exactly one 2-component (Carlson et al., 16 Jun 2026). The paper argues that 2-components capture cohesive “family blocks” that do not artificially split parent from child and can be computed in $N\approx 80$6 time (Carlson et al., 16 Jun 2026).

Temporal structure can also be inferred directly from topology through pseudogenerations. Writing the genealogy as a mixed graph $N\approx 80$7, the “pseudogeneration optimization problem” is

$N\approx 80$8

subject to $N\approx 80$9 for all parent–child arcs, equality constraints for singleton-union partners, and $M\approx 41.5$0 (Carlson et al., 16 Jun 2026). Because the parent–child graph is a DAG, feasibility and optimality follow, and the output labels each individual by an inferred generation layer (Carlson et al., 16 Jun 2026). Within this framework, the aggregate network exhibits consistent disassortative mixing, with observed $M\approx 41.5$1 and $M\approx 41.5$2, and recorded unions are strongly biased toward short genetic distances relative to potential pairings: cumulatively, $M\approx 41.5$3 of real unions occur within the closest $M\approx 41.5$4 of potential pairings (Carlson et al., 16 Jun 2026). Over pseudogenerations, $M\approx 41.5$5 falls from $M\approx 41.5$6 in the earliest layer to $M\approx 41.5$7 in the modern layer, while $M\approx 41.5$8 rises from $M\approx 41.5$9 to $< 2$00 (Carlson et al., 16 Jun 2026).

6. Demographic uses, data limitations, and terminological scope

Massive family trees have become a quantitative resource for population history. The WikiTree-based study reports decade-binned analyses of names, sex ratios, fertility, marriage patterns, and lifespan correlations, including an observed twin rate of $< 2$01 and triplet rate of $< 2$02, compared to Hellin’s approximation $< 2$03 and $< 2$04 (Fire et al., 2014). It also reports that “Wendy” rose from near zero pre-1900 to $< 2$05 of female births by 1950, that sons named after fathers rose to $< 2$06 in the 16th century and then declined, that mean maternal age at first birth rose from $< 2$07 years in 1700s to $< 2$08 years by 1900, and that spousal age-at-death correlation is $< 2$09 with $< 2$10 (Fire et al., 2014). These results show how genealogical corpora can be used to test century-old demographic and social hypotheses at unprecedented scale (Fire et al., 2014).

At the same time, the literature emphasizes persistent limitations. Aggressive disambiguation maximizes coverage but risks mislocated points; overlooking missing-geocode records can bias geographic coverage toward better-documented locales; and applying a gravity model without double-constraint yields marginal misfit (Koylu et al., 2020). Missing a sibling or marriage loses some loops, although long-tail loops are described as robust (Boyd et al., 2023). More generally, unresolved conflicts, incomplete parent pointers, and platform-specific documentation practices shape the observable network (Koylu et al., 2020, Carlson et al., 16 Jun 2026). This suggests that massive family trees are simultaneously data-rich and systematically censored.

A final terminological caution concerns the word “tree.” In genealogical network research, “family tree” refers to kinship data represented as graphs with parent-child and union relations (Boyd et al., 2023). In set theory, by contrast, a $< 2$11-tree is a tree of height $< 2$12 whose levels have size $< 2$13, and an Aronszajn tree is a $< 2$14-tree with no branch of length $< 2$15 (Krueger, 2021). Krueger’s “A Large Pairwise Far Family of Aronszajn Trees” constructs a family $< 2$16 of normal $< 2$17-complete $< 2$18-embeddable non-special $< 2$19-Aronszajn trees under specific set-theoretic hypotheses, a usage entirely distinct from genealogical analysis (Krueger, 2021). The shared term therefore masks two unrelated technical traditions: one concerns human kinship networks at population scale, and the other concerns combinatorial set theory.