Identification of the network structure of the Hebrew Bible texts based upon the notion of the otherworld and the afterlife

The study seeks to uncover hidden intertextual relations within the Hebrew Bible by focusing on how its texts conceptualize the otherworld and the afterlife. Motivated by growing applications of network science in social sciences, linguistics, and historical texts, the authors restrict the corpus to the Hebrew Bible (excluding apocrypha, pseudepigrapha, Qumran scrolls, and non-Jewish traditions) to avoid ambiguity. The research question is how key afterlife-related concepts are distributed across texts and how these shared concepts define a network structure, clusters, and influential texts in the development of Israelite/Judahite notions of the afterlife. The purpose is to quantify conceptual overlaps, reveal community structures among texts, and identify conceptually central works. The significance lies in offering a quantitative, network-based perspective on the evolution and interconnection of afterlife concepts in the Hebrew Bible—an area less explored compared to New Testament-centered network analyses.

The paper situates itself within network science applications in the humanities and social sciences. Foundational studies of social networks (Read 1954; Sampson 1969; Padgett & Ansell 1993; Milgram 1967) and applications to language (Ferrer i Cancho & Solé 2001; Wachs Lopes & Rodrigues 2016; Corrêa et al. 2018) and historical/religious texts (Serif 2023; Choi & Kim 2007; Elwert 2021) are reviewed. In Biblical studies, network analyses often focus on Jesus and first-century Christianity (Duling 2002; Czachesz 2016; McClure 2018), with less attention to the Hebrew Bible. A relevant prior approach using signed networks examined relationships among early Jewish religious/philosophical movements (Tantlevskij et al. 2021), showing a trend toward balanced structures. This paper extends beyond describing pre-existing networks to constructing a conceptual network centered on afterlife notions specifically within the Hebrew Bible corpus.

- Corpus and concepts: The authors identified 43 Hebrew Bible texts containing afterlife concepts: Genesis, Numbers, Deuteronomy, Judges, 1–2 Samuel, 2 Kings, Proto-Isaiah, Deutero-Isaiah, Jeremiah, Ezekiel, Hosea, Malachi, Psalms (6, 16, 17, 21, 23, 27, 30, 36, 37, 41, 49, 55, 56, 61, 73, 88, 94, 103, 106, 110, 116, 119, 139, 142, 143), Job, Proverbs, Qoheleth, Daniel, and 2 Chronicles. - Concept taxonomy: A set of 24 tagged concepts (Table 1) was compiled covering Sheol as universal destination (Sh_all), differentiation in Sheol, joining one’s people, pre-mortem descent of the wicked, ascension-to-heaven for the righteous vs others to Sheol (Sh_others), rapture of the most righteous (Ascension_to_heaven), afterlife deification, national separation in Sheol, degrees of identity, feeling, appearance retention in Sheol, Sheol as dull existence and lack of contact with God, possibility of contact with God, loss of individuality/Avaddon, spirit vs flesh, judgment in Sheol (Lord_justice), true immortality, human spirit as bearer of selfness, resurrection (bodily), interim abodes before resurrection (Sheol or heaven), and selected non-resurrection for extreme sinners. In total, 112 text–concept pairs were identified (full mapping in Supplementary Materials). - Network construction: Texts are vertices; an undirected edge connects two texts if they share at least one concept; edge weight equals the number of shared concepts. This yields a weighted graph of conceptual overlap. - Descriptive statistics: The graph has 43 vertices and 383 edges; total edge-weight sum 462; average degree ≈ 17.8; density 0.424; degree distribution shows a large peak at 23 and smaller peaks at 6 and 27. - Community detection: The Louvain algorithm (modularity maximization) partitions the network into three clusters. - Vertex ranking: Four ranking methods were applied to identify influential texts: PageRank, HITS, quasi-exponential ranking (linear), and exponential ranking (non-linear). Rankings are compared to assess invariance of influential vertices across methods.

- Network structure: Highly interconnected network (density 0.424) with 43 vertices, 383 edges, total weight 462, average degree ≈ 17.8. Degree distribution is non-uniform (peaks at 6, 23, 27). - Louvain clustering into three groups: Group 1: Genesis, Numbers, Deuteronomy, 1 Samuel, Judges, 2 Kings, Proto-Isaiah, Deutero-Isaiah, Jeremiah, Ezekiel, Psalms 55 and 106, Daniel, 2 Chronicles. Characteristic concepts include Sh_join_people, Resurrection, Afterlife_deification (diverse conceptual set; may warrant further subdivision). Group 2: 2 Samuel; Psalms 6, 30, 88, 94; Job; Qoheleth. Characterized by Sh_dull_existence and Sh_no_contact_with_God (negative portrayal of Sheol). Group 3: Hosea, Malachi; Psalms 16, 17, 21, 23, 27, 36, 37, 41, 49, 56, 61, 73, 103, 110, 116, 119, 139, 142, 143; Proverbs. Characterized by Ascension_to_heaven and Sh_others (righteous ascend; others to Sheol). - Influential texts (vertex ranking): • PageRank/HITS/quasi-exponential (top five with minimal variation): Proto-Isaiah; Qoheleth; Job; Proverbs; 1 Samuel. • Exponential ranking (non-linear): Ezekiel; Genesis; 1 Samuel; Qoheleth; Job. These texts tend to have high concept counts: Proto-Isaiah (12); Qoheleth (9); Job (9); Ezekiel (9); Genesis (8); Proverbs (5); 1 Samuel (5). - Conceptual correlates of influence: The most influential texts commonly include Sh_others and Ascension_to_heaven. Additional concepts frequently associated with top-ranked texts: Lord_justice, Sh_dull_existence, True_immortality, Human_spirit_bears_selfness, Sh_identity. Notably, frequently occurring concepts like Sh_join_people and Resurrection are not necessarily “important” in rankings, indicating that importance is not solely a function of frequency. - Interpretation: The network reveals strong intertextual connections and suggests that key texts (Proto-Isaiah, Qoheleth, Job, Proverbs, 1 Samuel, Ezekiel, Genesis) centrally shaped the development of Jewish afterlife conceptions.

The findings address the research question by mapping how shared afterlife concepts forge intertextual ties across the Hebrew Bible. The dense connectivity indicates substantial conceptual overlap and likely mutual influence. Community detection highlights thematically coherent clusters: one emphasizing ascension/reward vs descent (Group 3), another emphasizing Sheol’s negativity and separation from God (Group 2), and a diverse, historically central cluster containing legal-historical and prophetic texts (Group 1). Ranking results converge on an invariant set of influential texts (Proto-Isaiah, Qoheleth, Job, Proverbs, 1 Samuel, Ezekiel, Genesis), indicating robustness to algorithm choice and suggesting these works are central hubs in the conceptual transmission and evolution of afterlife ideas. The analysis underscores a historical trajectory toward intensifying preservation of personal identity (first spiritual, later coupled with bodily resurrection) and an increasingly explicit ethical framework of posthumous reward and punishment. These insights demonstrate how network methods can reveal both macro-structures (clusters) and key actors (influential texts) in the development of theological concepts.

This study introduces a graph-theoretic framework to analyze afterlife-related concepts across the Hebrew Bible, constructing a weighted intertextual network, detecting communities, and identifying influential texts via multiple ranking algorithms. It reveals three conceptually coherent clusters and an invariant set of central texts (Proto-Isaiah, Qoheleth, Job, Proverbs, 1 Samuel, Ezekiel, Genesis). The work shows that conceptual importance is not strictly tied to frequency and that afterlife notions evolve toward a stronger emphasis on personal identity and ethical judgment. Future research directions include expanding the corpus to apocrypha and pseudepigrapha, Dead Sea Scrolls, the New Testament, early Christian and Rabbinic literature, and investigating mathematical properties such as ranking invariance more systematically.

- Corpus restriction: The study deliberately excludes apocrypha, pseudepigrapha, Qumran scrolls, and non-Jewish traditions, potentially omitting influential intertexts. - Concept identification: Mapping 112 text–concept pairs relies on scholarly interpretation; some passages (e.g., Sheol-related rhetoric) are ambiguous and may affect coding. - Granularity: Treating entire books or selected psalms as single vertices may mask intra-textual variability across passages or redactional layers. - Clustering resolution: Group 1 is diverse and may require further decomposition; community assignments can vary with algorithm parameters. - Contextual factors: The study does not model sociological settings or historical transmission pathways that could nuance intertextual influence. - Generalizability: Findings pertain to the Hebrew Bible corpus as defined; extending to broader corpora may alter network structure and rankings.