BibVik — Part 3: Joining structural and annotation descriptions
Strategy and method — working document, 2026-07-03
This document renders the full analysis by including each stage in sequence. Each stage is also a standalone .qmd and can be read, edited, or rendered independently. See 00_plan.qmd, 01_annotation.qmd, 02_network_structure.qmd, 03_joined_descriptions.qmd. Girvan-Newman runs separately, outside this chain entirely — see gn_analysis/README.md.
Executed analysis lives in separate files:
01_annotation.qmd— annotation cross-tab (F1 corpus), independent of the citation graph02_network_structure.qmd— degree, centrality, k-core, components, Louvain, Leiden, k-means on centrality profiles (GN excluded — see below)gn_analysis/— Girvan-Newman, run standalone on the remote server via tmux, outside the Quarto render chain entirely (seegn_analysis/README.md)03_joined_descriptions.qmd— places the annotation and structural descriptions side by side
This document holds only the analytical plan and reasoning; no executed code.
Status
This is a single working document combining the analytical plan with the code and outputs that carry it out. Several conceptual questions below are resolved; several concrete decisions (final scope of Girvan-Newman, whether to add directionality, which alternative unit of analysis to pursue first) are deliberately still open and marked as such. Sections without code are strategy and reasoning; sections with code are live analysis.
Starting point
The original motivating question, from the seed paper (Lund & Sindbæk 2022): does the field divide into something like two camps around the origin of the Viking Age, along lines that co-vary across gender, topic, method and sources of evidence?
This is a substantive, testable proposition from the literature — worth distinguishing from the research team’s own fieldwork-based instincts about where the data might be heading (e.g. topic/gender associations noticed informally in the field). Both are legitimate to bring to this analysis, but they carry different epistemic weight and should be kept distinct in any eventual writeup: one is a claim to confirm or complicate; the other is an interpretive lens the team brings to reading whatever the data shows.
Core methodological stance: no baseline, just independent descriptions
This is not a search for deviation from an expected or random pattern. The dataset is historically and socially situated — citation clustering along social, institutional, or intellectual lines is the expected, produced-by-history outcome, not an anomaly standing out against a null model. This is a real objection to modularity-based community detection (Louvain, Leiden), whose optimization target is explicitly “more clustered than a random graph with the same degree sequence would be.” That framing is not a neutral default for this kind of data.
The working alternative, used throughout this document: treat every computed structure — citation-graph community structure, the annotation cross-tab, per-work citer profiles, direct homophily rates — as an independent, self-contained description of the corpus, computed on its own terms with no reference point implied. None is privileged as ground truth against which another is checked. The actual analytical content is in the relationship between these descriptions once more than one exists: agreement, disagreement, partial overlap, or cross-cutting are all just facts about that relationship, not confirmations or violations of anything. This is the logic behind treating the annotation data as something to “bolt on” to a citation-structure analysis, rather than using one to validate the other, and it governs how every result below should be read.
Why Girvan-Newman over modularity methods, for the “camps” question
Louvain and Leiden are fast (near-linear time, tractable at any scale without special hardware) and were considered as a way around Girvan-Newman’s poor scalability. Both are computed below as additional independent descriptions, but neither is treated as the primary method for the “camps” question specifically, for reasons distinct from performance:
- Their optimization target (deviation from a random-graph null model) is the wrong lens for socially/historically produced structure, per above.
- The “camps” question is specifically about whether the graph splits cleanly, and in what order — a first split into two, each of which may or may not split further into more nuanced sub-divisions. Girvan-Newman’s hierarchical, edge-removal structure encodes exactly this nesting as a byproduct of how it runs; a flat modularity partition does not answer “is two-way division the first-order truth” as directly.
Louvain/Leiden are computed as additional, independent descriptions in their own right — not as a faster substitute for Girvan-Newman, and not as a “cross-check” implying agreement would validate either method. The two families of method ask different structural questions (dense-cluster membership vs. load-bearing bridges) and can legitimately produce different, non-comparable pictures of the same graph. Their disagreement, if any, is reported as a finding, not a discrepancy to resolve.
Girvan-Newman tractability
The problem. Full Girvan-Newman decomposition is expensive because edge betweenness centrality must be recomputed after every single edge removal — this is inherently sequential across iterations (removal i+1 depends on the graph state after removal i), so parallelizing across iterations is not possible. An earlier assessment that GN “can’t really be parallelized” on an available 84-core server is only half right.
What does parallelize. The betweenness calculation within a single iteration (Brandes’ algorithm) sums independent per-source-node contributions, and is embarrassingly parallel across those source nodes. graph-tool supports this; a networkx-based multiprocessing wrapper could achieve something similar. This would meaningfully speed up the expensive per-iteration cost, without approximating anything — every node, including low-degree ones, remains fully part of the calculation. Not yet implemented in the code below — the current implementation uses igraph::cluster_edge_betweenness() as-is, which does not parallelize the per-iteration cost. This should be revisited if runtime on the full graph proves impractical.
Rejected optimization: peeling degree-1 (leaf) nodes, or pre-filtering to a k-core, before running GN. Considered and explicitly rejected. Leaves (or low-coreness nodes generally) are cheap to strip and their community assignment could be trivially inferred afterward from their highest-degree neighbor — but this is a real approximation, not a free win:
- Leaves attached to a neighbor whose own community assignment is itself marginal/unstable would inherit an arbitrary decision.
- Leaf-peeling cascades: removing one leaf can drop a neighbor to degree 1, triggering further removal, which can strip small but genuine citation chains, not just pendant noise.
- Removing leaves changes the betweenness values of the edges that remain, since leaves still contribute path endpoints to the full-graph calculation — the pruned-graph result is not guaranteed to approximate the full-graph result closely.
- Most importantly for this project: a paper cited only once may be exactly the interesting case (niche, contested, or newly-emerging reference) for a study of citational politics, not noise to discard. Peripheral/rarely-cited nodes are data, not overhead, given the research question explicitly concerns how peripheral material relates to dominant positions.
Current direction: bounded-depth GN on the full, unfiltered graph. Rather than decomposing to individual papers, or filtering the input graph first, the edge-removal process is read off at the first several splits (e.g. first split, then the splits within each resulting side), computed on every node in the graph. This is not merely a performance compromise — the first few splits are the more interpretable structural fact for the “camps” question; full decomposition to singleton papers stops being a meaningful description of factional structure at all. This is implemented below; whether it is fast enough on the full graph without the parallelization described above has not yet been benchmarked.
Time and directionality
The F1 corpus spans a single decade — too short to usefully time-slice without each slice becoming too sparse to support reliable community detection or homophily estimates. Time-sliced structural analysis and homophily-as-a-trend-over-time were both considered and set aside for this reason, not because time is uninteresting in principle.
Directionality remains open and is a separate matter from time-slicing. The citation graph is directed (citer → cited); the community-detection methods below are run on the undirected projection (standard practice for this class of algorithm, and consistent with the centrality measures, which are computed in directed form separately). Whether “who is drawn upon vs. who does the drawing” should be built into the community-detection step itself, using directed variants of GN/Louvain/Leiden, is not yet decided.
F2 publication date at time of citation is a separate small thread worth keeping in mind: F2 works are not bound by the F1 decade and may span a much longer history. Whether the age of cited material varies systematically depending on which part of the F1 corpus is doing the citing is a fact already present in the data (publication years) without requiring any time-slicing of the corpus itself. Not yet implemented below.
The independent descriptions computed in this document
Consistent with the no-baseline stance, the analysis is organized as a set of independently computable, independently meaningful descriptions of the corpus, to be placed alongside each other rather than run in a required sequence. This document computes:
Structural descriptions of the citation graph — degree, centrality (betweenness, closeness, PageRank, HITS), k-core, connected components, and community detection (Girvan-Newman, Louvain, Leiden, k-means on centrality profiles). See below.
The annotation cross-tab — author gender × primary/secondary topic × primary/secondary method, across the F1 corpus. Tests whether the seed paper’s supposed tripartite co-variation is visible in the coded data at all. Computed independently of any graph work.
Not yet implemented in this document, recorded here so the plan is not lost:
Per-F2-node citer profiles. For F2 works cited by multiple F1 papers, characterize the citer set using annotation data that exists only on the F1 side: gender composition, topic/method diversity, and whether the citer set is itself structurally clustered or scattered. Does not require resolving the community-detection method question and is tractable immediately once prioritized. Speaks to a genuinely different citational-politics phenomenon than the corpus-wide cross-tab: whether particular sources function as shared/foundational touchstones cited across the field’s internal divisions, or as in-group markers cited mainly within one part of it.
Direct citation homophily. Do papers (or, at the author level — see “alternative units” below — authors) disproportionately cite others sharing their coded gender/topic/method characteristics? A direct join of two already-independent descriptions (citation edges, annotation data) with no algorithmic mediation in between. Likely the most immediately tractable of the not-yet-built analyses.
Joining structural and annotation descriptions. Whether Girvan-Newman’s top-level split(s), Louvain communities, and Leiden communities correspond to, cut across, or ignore the coded categories; whether centrality within a community correlates with author gender even when a community’s dominant topic is not itself gender-skewed.
Extension for future consideration: alternative units of analysis
Everything in this document treats the paper as the unit of the graph (papers cite papers). This is one particular projection of a richer structure, not the only one, and is worth extending in future work — not resolved or prioritized now, but recorded so it isn’t lost:
Author-level graphs. Collapsing papers into authors changes what centrality means (a prolific author becomes a hub independent of any single paper’s standing) and makes author-to-author citation homophily a more natural unit than paper-to-paper for gender-citation questions. Co-authorship itself becomes an additional structural question: do co-authorships cross or reinforce whatever divisions appear elsewhere.
Venue-level graphs (journal, edited volume, conference proceedings, grey literature/excavation report). Likely to reveal institutional or disciplinary structure rather than intellectual structure directly, and could complicate a purely topic/gender reading — a “camp” might partly reflect which kind of venue a sub-field mostly publishes in, particularly given the corpus’s substantial non-English, non-journal material (excavation reports, conference proceedings).
Kind-of-work as a unit (monograph vs. article vs. excavation report vs. edited-volume chapter). Related to venue but not identical; may track disciplinary/generational norms that could explain or cross-cut part of any gender/topic pattern rather than sitting alongside it as a fully independent axis.
Each alternative unit would be, again, an independent description rather than a more “real” or authoritative one. A useful way to stress-test any finding at the paper level is to check whether it persists, sharpens, or dissolves when re-aggregated to authors or venues — if a division only appears at one level of aggregation, that is itself informative about whether the division is fundamentally about individual works, about people, or about where people publish.
Strategy and reasoning for this analysis: see 00_plan.qmd.
This section computes the annotation cross-tab entirely independently of the graph work above — no reference to citation structure, communities, or centrality. Per the no-baseline stance, this is not a check against Part 1; it stands on its own, and Part 3 (below) is where the two are placed side by side.
Publications per year
Gender by first author and all authors
Publications by gender for each year. Single-author work vs. collaborations have not yet been examined separately.
Multi-author gender composition and author order
The analyses above use first-author gender only (for the topic/method/source cross-tabs later in this document) or a flattened, order-blind pool of all author genders (the “all authors” plot). Neither captures gender composition per paper (all-male vs. all-female vs. mixed) or order within a paper, both of which are needed for the co-authorship questions raised in planning (do co-authorships cross or reinforce whatever divisions appear elsewhere; does the most senior/lead author’s gender matter independently of the full author-list composition).
Author order is genuinely ambiguous in this corpus and must be handled carefully, not with a single fixed rule. Field convention varies: first-author-as-lead is standard for excavation/fieldwork-based publications, but last-author-as-lead (PI convention) is standard for lab-based work. Which convention applies depends on the paper’s own method — one of the coded variables, not something inferable from the author list alone. The lookup below (fieldwork_lead_methods) is a placeholder mapping specific coded method categories to the convention that applies; it must be filled in with the actual method category names from the codebook before this analysis is meaningful. Left unmapped, methods default to “ambiguous” and are excluded from any lead-author-specific analysis (though still included in the order-blind composition analysis below).
This section works generically across however many Authors..Genders..Author.N. columns exist in the data — no fixed column count is assumed.
Detected 5 author-position gender columns:[1] "Authors..Genders..Author.1." "Authors..Genders..Author.2."
[3] "Authors..Genders..Author.3." "Authors..Genders..Author.4."
[5] "Authors..Genders..Author.5."| n_authors | n |
|---|---|
| 1 | 223 |
| 2 | 61 |
| 3 | 25 |
| 4 | 18 |
| 5 | 38 |
| 6 | 1 |
| 9 | 1 |
Candidate gender-composition categorizations
Several ways of collapsing a per-paper gender sequence into a single cross-tabbable category are computed side by side below, since it is not yet decided which is most useful. This is a case of comparing several independent categorization schemes against the same underlying data, not picking the “correct” one — inspect the resulting distributions before choosing.
| composition_strict | n |
|---|---|
| all-female | 119 |
| all-male | 159 |
| includes uncertain | 6 |
| mixed | 83 |
| composition_majority | n |
|---|---|
| balanced | 27 |
| includes uncertain | 6 |
| majority-female | 148 |
| majority-male | 186 |
| composition_singleauthor_split | n |
|---|---|
| all-female (multi-author) | 20 |
| all-male (multi-author) | 35 |
| includes uncertain | 6 |
| mixed | 83 |
| solo-female | 99 |
| solo-male | 124 |
Gender composition by primary topic, method, and source of evidence
Unlike the first-author-only cross-tabs later in this document, this uses the composition categories above — bringing multi-author, order-aware gender data into the same kind of comparison already done for first-author gender. composition_strict is used here as a starting point; swap in composition_majority or composition_singleauthor_split to compare.
Not yet done, worth noting: the topic/method/source cross-tabs above use primary values only, same limitation as the first-author-only cross-tabs later in this document — secondary topic/method/source values are not yet brought into any gender comparison. Extending composition_topic/composition_method/composition_source to include secondary values would mean joining on both Primary and Secondary counts rather than filtering to Primary only, and deciding how to weight or display a paper that contributes to multiple topics at once.
Primary topic, in aggregate and over time
Primary method, in aggregate and over time
Primary sources of evidence, in aggregate and over time
Secondary topics by primary topic
Secondary methods by primary method
Secondary sources of evidence by primary source of evidence
Primary topic by first author gender
This is the first of the three plots most directly relevant to the seed paper’s tripartite (gender/topic/method) supposition. Normalizing each topic’s proportions against the corpus-wide gender base rate has been discussed as a follow-up refinement but not yet implemented — the raw proportions below do not yet control for the overall gender imbalance in the corpus.
Primary method by first author gender
Primary source of evidence by first author gender
Region
Strategy and reasoning for this analysis: see 00_plan.qmd.
Girvan-Newman is run separately, outside this document — see gn_analysis/README.md. Its output (gn_analysis/results/communities.csv) can be read in here once available; see the commented-out read-in at the end of this file.
Part 2 — Citation graph: structural descriptions
Setup
Nodes: 14331 Edges: 24635 Directed: TRUE Density: 0.0001199582 Ghost nodes (tombstoned entries retained for edge preservation): 0 Degree and centrality
In-degree (times cited within the corpus) and out-degree (number of works cited) capture different roles. High in-degree identifies widely-cited works — the intellectual anchors of the field. High out-degree identifies works that are heavily engaged with the literature, drawing on many sources.
Betweenness centrality identifies works that sit on many shortest paths between other works — brokers between sub-literatures. Betweenness is expensive to compute on large graphs; normalized values are reported.
PageRank assigns authority based on incoming links weighted by the authority of the linking node — conceptually similar to being cited by works that are themselves widely cited. Hub and authority scores (HITS) are complementary: hubs point to many authorities; authorities are pointed to by many hubs.
Peripheral works — low degree, low centrality by every measure below — are not treated as noise in this project. A work cited only once may be exactly the interesting case (a niche, contested, or newly emerging reference) for a study of citational politics. No node is excluded from any measure in this section on the basis of low degree.
Most cited (by in-degree)
| name | title | year | generation | in_degree |
|---|---|---|---|---|
| smith2020 | Migrant Identities and Funerary Practices: An Archaeological Perspective | 2020 | F2 | 100 |
| price2002 | The Viking way: religion and war in late Iron Age Scandinavia, Uppsala. Price, Neil In press: The archaeology of seiðr: circumpolar traditions in Viking pre-Christian religion | 2002 | F1 | 75 |
| unesco2019 | Hedeby Harbour: Insights into Long Distance Trade and Maritime Practices | 2019 | F2 | 44 |
| skre2007 | Towns and Markets, Kings and Central Places in South-Western Scandinavia C. Ad 800-950 | 2007 | F2 | 43 |
| svanberg2003 | Death rituals in south-east Scandinavia AD 800-1000: Decolonizing the Viking Age 2. Stockholm: Almqvist and Wiksell International. häte, Eva 2007. Monuments and minds: monument re-use in Scandinavia in the second half of the irst millennium AD | 2003 | F1 | 42 |
| sindbaek2007 | 2007a. he Small World of the Vikings: Networks in Early Medieval Communication and Exchange | 2007 | F1 | 34 |
| brink2008 | Lord and Lady -Bryti and Deigja: some historical and etymological aspects of family, patronage and slavery in early Scandinavia and Anglo-Saxon England | 2008 | F2 | 32 |
| price2010 | Kings and commoners at copán: isotopic evidence for origins and movement in the classic maya period | 2010 | F1 | 26 |
| arbman1940 | Birka. Untersuchungen und Studien. 1. Die Gräber: Tafeln. Stockholm: Vitterhets-, historie-och antikvitetsakademien | 1940 | F2 | 26 |
| price2008 | Routledge, London. 2008b. Bodylore and the Archaeology of Embedded Religion: Dramatic License in the Funerals of the Vikings | 2008 | F1 | 25 |
| barrett2008 | Detecting the Medieval Cod Trade: A New Method and First Results | 2008 | F1 | 24 |
| skre2008 | Dark Age Towns: The Kaupang Case. Reply to Przemysław Urbańczyk | 2008 | F1 | 24 |
| hedeager2011 | Iron Age Myth and Materiality: An Archaeology of Scandinavia AD 400-1000. L and | 2011 | F1 | 23 |
| feveile2006 | ASR 1000 Ribelund II, in Det AEldste Ribe: Udgravninger på Nordsiden af Ribe Å 1984-2000, ed. C. Feveile. (Ribe Studier 1.2.) Aarhus: Jysk Arkaeologisk Selskab | 2006 | F2 | 23 |
| hedeager1999 | Deposition of wealth in the cultura l landscape. glyfer och arkeolog iska rum -en viinbok till jar! nordbladh | 1999 | F2 | 22 |
| sindbaek2011 | Silver economies and social ties: Long-distance interaction, long-term investments -And why the Viking Age happened | 2011 | F1 | 21 |
| solli2002 | Herskermaktens ritualer. kan mytologien sette oss på spor av riter, gjenstander og kult knyttet til herskerens intronisasjon? | 2002 | F1 | 21 |
| gustin2004 | The Coins and Weights from the Excavations 1990-1995. An Introduction and Presentation of the Material. Eastern connections. Excavations in the black earth 1990-1995. P. 2, Numismatics and metrology | 2004 | F2 | 21 |
| zachrisson1998 | Gård, gräns och gravfält, sammanhang kring ädelmetalldepåer och runstenar från vikingatid och tidigmedeltid i uppland och gästrikland. stockholm studies in archaology 15 | 1998 | F2 | 21 |
| barrett2004 | Identity, gender, religion, and economy: New isotope and radiocarbon evidence for marine resource intensification in Early Historic Orkney, Scotland, UK | 2004 | F2 | 21 |
Most citing (by out-degree)
| name | title | year | generation | out_degree |
|---|---|---|---|---|
| NOAUTHOR24 | F1 | 1113 | ||
| lund2021 | Crossing the Maelstrom: New Departures in Viking Archaeology | 2021-05-15 | P | 570 |
| weissnd | Stettin Os ´rodek Archeologii S ´redniowiecza Krajów Nadbałtyckich Instytut Archeologii i etnologii pAN Wien Österreichische Nationalbibliothek gEfördErt durcH | F1 | 480 | |
| raffield2019 | Playing Vikings: Militarism, hegemonic masculinities, and childhood enculturation in Viking Age Scandinavia | 2019 | F1 | 264 |
| croix2019 | Single Context, Metacontext, and High Definition Archaeology: Integrating New Standards of Stratigraphic Excavation and Recording | 2019 | F1 | 252 |
| anchukaitis2017 | Last millennium Northern Hemisphere summer temperatures from tree rings: Part II, spatially resolved reconstructions | 2017 | F1 | 226 |
| NOAUTHOR28 | Kaupanghave Qualified for Classification as Prototowns or Emporia, According to Frankish and Anglo-Saxon Terms and Models ( | F1 | 195 | |
| gardela2018 | Amazons of the North? Armed females in Viking archaeology and medieval literature | 2018 | F1 | 184 |
| bill2019 | 5. The Ship Graves on Kormt – and Beyond | 2019 | F1 | 174 |
| price2019 | Vikings in Russia: Origins of the medieval inhabitants of Staraya Ladoga | 2019 | F1 | 168 |
| price2018 | Multi-Isotope Proveniencing of Human Remains from a Bronze Age Battlefield in the Tollense Valley in Northeast Germany | 2018 | F1 | 167 |
| croix2015 | The Vikings, Victims of their Own Success? A Selective View on Viking Research and its Dissemination | 2015 | F1 | 165 |
| raffield2016 | Male-Biased Operational Sex Ratios and the Viking Phenomenon: An Evolutionary Anthropological Perspective on Late Iron Age Scandinavian Raiding | 2016 | F1 | 165 |
| raffield2018 | Polygyny, concubinage and the social lives of women in Viking Age Scandinavia | 2018 | F1 | 160 |
| solli2011 | The archaeology of ice. Finds from the Frozen Past. Exhibition in Historical Museum | 2011 | F1 | 158 |
| knudson2012 | Migration and Viking Dublin: Paleomobility and paleodiet through isotopic analyses | 2012 | F1 | 156 |
| hartman2017 | Medieval Iceland, Greenland, and the New Human Condition: A case study in integrated environmental humanities | 2017 | F1 | 154 |
| milek2012 | Floor Formation Processes and the Interpretation of Site Activity Areas: An Ethnoarchaeological Study of Turf Buildings at Thvera, Northeast Iceland | 2012 | F1 | 153 |
| skre2019 | Rulership in 1st to 14th Century Scandinavia: Royal Graves and Sites at Avaldsnes and Beyond, Ergänzungsbände zum Reallexikon der Germanischen Altertumskunde | 2019 | F1 | 148 |
| barrett2010 | Rounding up the usual suspects: Causation and the Viking Age diaspora | 2010 | F1 | 146 |
Degree distribution
A power-law or scale-free degree distribution is characteristic of citation networks: most works are cited rarely, a small number are cited frequently. The log-log plot tests this.
Top by betweenness centrality
Works with high betweenness mediate between otherwise disconnected parts of the citation network — likely works that bridge sub-fields or periods.
| name | title | year | betweenness |
|---|---|---|---|
| price2010 | Kings and commoners at copán: isotopic evidence for origins and movement in the classic maya period | 2010 | 0.0012 |
| price2018 | Multi-Isotope Proveniencing of Human Remains from a Bronze Age Battlefield in the Tollense Valley in Northeast Germany | 2018 | 0.0012 |
| carver2015 | Commerce and cult: Confronted ideologies in 6th-9th-century Europe | 2015 | 0.0012 |
| gullbekk2014 | Vestfold: A monetary perspective on the Viking Age | 2014 | 0.0008 |
| skre2017 | Monetary practices in early medieval western Scandinavia (5th-10th centuries AD) | 2017 | 0.0008 |
| skre2019 | Rulership in 1st to 14th Century Scandinavia: Royal Graves and Sites at Avaldsnes and Beyond, Ergänzungsbände zum Reallexikon der Germanischen Altertumskunde | 2019 | 0.0007 |
| baug2019 | The beginning of the Viking Age in the West | 2019 | 0.0007 |
| ashby2015 | What really caused the Viking Age? The social content of raiding and exploration. Archaeological Dialogues | 2015 | 0.0006 |
| hilberg2014 | Viking Age Hedeby and its relations with Iceland and the North Atlantic: Communication, long-distance trade, and production | 2014 | 0.0004 |
| hadley2016 | radiocarbon dates for the cist graves are AD 1030-1210 and AD 1025-1165 | 2016 | 0.0003 |
| rogers2020 | Non-ferrous metalworking networks in Scandinavian-influenced towns of Britain and Ireland | 2020 | 0.0003 |
| croix2015 | The Vikings, Victims of their Own Success? A Selective View on Viking Research and its Dissemination | 2015 | 0.0003 |
| gardela2015 | Uzbrojona kobieta z truso. Nowe rozważania nad miniaturami tzw. walkirii z epoki wikingów’ (The Armed Female from truso | 2015 | 0.0003 |
| price2011 | Who was in Harold Bluetooth´s army? Strontium isotope investigation of the cemetery at the Viking Age fortress at Trelleborg, Denmark. Antiquity | 2011 | 0.0003 |
| price2014 | Galgedil: Isotopic studies of a Viking cemetery on the Danish island of Funen, AD 800-1050 | 2014 | 0.0002 |
| raffield2016 | Male-Biased Operational Sex Ratios and the Viking Phenomenon: An Evolutionary Anthropological Perspective on Late Iron Age Scandinavian Raiding | 2016 | 0.0002 |
| perry2016 | Pottery production in Anglo-Scandinavian Torksey (Lincolnshire): Reconstructing and contextualising the chaîne opératoire | 2016 | 0.0002 |
| sindbaek2017 | Urbanism and exchange in the North Atlantic/Baltic, 600-1000 CE | 2017 | 0.0002 |
| raffield2014 | A River of Knives and Swords’: Ritually Deposited Weapons in English Watercourses and Wetlands During the Viking Age | 2014 | 0.0001 |
| eriksen2013 | Doors to the dead: The power of doorways and thresholds in Viking Age Scandinavia | 2013 | 0.0001 |
Connected components
A weakly connected component (WCC) treats edges as undirected. A strongly connected component (SCC) requires paths in both directions — rare in citation networks, since citations are historically directed (a 2010 paper cannot cite a 2020 paper). The WCC structure shows how fragmented the network is; a dominant giant component indicates a well-connected literature.
Weakly connected components: 1 Largest WCC: 14331 nodes ( 100 % of graph)Strongly connected components: 14302 Largest SCC: 22 nodesWCC size distribution
| size | n |
|---|---|
| 14331 | 1 |
K-core decomposition
The k-core of a graph is the maximal subgraph in which every node has at least k connections to other nodes within that subgraph. It is computed by iteratively removing nodes with degree below k until no further removal is possible. Nodes are assigned a coreness value equal to the highest k for which they remain in the k-core.
K-core decomposition is reported here purely as a descriptive measure — identifying which works are structurally embedded in dense mutual-citation relationships versus which sit at the periphery. It is not used below as a preprocessing filter for any other method; every peripheral node (coreness = 1, or excluded entirely from any k ≥ 2 core) remains a full participant in every other analysis in this document, including Girvan-Newman.
Reference: Alvarez-Hamelin et al. (2005). Large scale networks fingerprinting and visualization using the k-core decomposition. Advances in Neural Information Processing Systems, 18.
Coreness distribution:
1 2 3 4 5 6 7 8 9
10269 1935 756 362 245 179 114 155 316 | coreness | n | mean_in_degree |
|---|---|---|
| 9 | 316 | 9.38 |
| 8 | 155 | 6.70 |
| 7 | 114 | 6.20 |
| 6 | 179 | 5.31 |
| 5 | 245 | 4.68 |
| 4 | 362 | 3.95 |
| 3 | 756 | 2.99 |
| 2 | 1935 | 2.00 |
| 1 | 10269 | 1.00 |
| name | title | year | coreness | in_degree |
|---|---|---|---|---|
| smith2020 | Migrant Identities and Funerary Practices: An Archaeological Perspective | 2020 | 9 | 100 |
| price2002 | The Viking way: religion and war in late Iron Age Scandinavia, Uppsala. Price, Neil In press: The archaeology of seiðr: circumpolar traditions in Viking pre-Christian religion | 2002 | 9 | 75 |
| unesco2019 | Hedeby Harbour: Insights into Long Distance Trade and Maritime Practices | 2019 | 9 | 44 |
| skre2007 | Towns and Markets, Kings and Central Places in South-Western Scandinavia C. Ad 800-950 | 2007 | 9 | 43 |
| svanberg2003 | Death rituals in south-east Scandinavia AD 800-1000: Decolonizing the Viking Age 2. Stockholm: Almqvist and Wiksell International. häte, Eva 2007. Monuments and minds: monument re-use in Scandinavia in the second half of the irst millennium AD | 2003 | 9 | 42 |
| sindbaek2007 | 2007a. he Small World of the Vikings: Networks in Early Medieval Communication and Exchange | 2007 | 9 | 34 |
| brink2008 | Lord and Lady -Bryti and Deigja: some historical and etymological aspects of family, patronage and slavery in early Scandinavia and Anglo-Saxon England | 2008 | 9 | 32 |
| price2010 | Kings and commoners at copán: isotopic evidence for origins and movement in the classic maya period | 2010 | 9 | 26 |
| arbman1940 | Birka. Untersuchungen und Studien. 1. Die Gräber: Tafeln. Stockholm: Vitterhets-, historie-och antikvitetsakademien | 1940 | 9 | 26 |
| price2008 | Routledge, London. 2008b. Bodylore and the Archaeology of Embedded Religion: Dramatic License in the Funerals of the Vikings | 2008 | 9 | 25 |
| barrett2008 | Detecting the Medieval Cod Trade: A New Method and First Results | 2008 | 9 | 24 |
| skre2008 | Dark Age Towns: The Kaupang Case. Reply to Przemysław Urbańczyk | 2008 | 9 | 24 |
| hedeager2011 | Iron Age Myth and Materiality: An Archaeology of Scandinavia AD 400-1000. L and | 2011 | 9 | 23 |
| feveile2006 | ASR 1000 Ribelund II, in Det AEldste Ribe: Udgravninger på Nordsiden af Ribe Å 1984-2000, ed. C. Feveile. (Ribe Studier 1.2.) Aarhus: Jysk Arkaeologisk Selskab | 2006 | 9 | 23 |
| hedeager1999 | Deposition of wealth in the cultura l landscape. glyfer och arkeolog iska rum -en viinbok till jar! nordbladh | 1999 | 9 | 22 |
| sindbaek2011 | Silver economies and social ties: Long-distance interaction, long-term investments -And why the Viking Age happened | 2011 | 9 | 21 |
| solli2002 | Herskermaktens ritualer. kan mytologien sette oss på spor av riter, gjenstander og kult knyttet til herskerens intronisasjon? | 2002 | 9 | 21 |
| gustin2004 | The Coins and Weights from the Excavations 1990-1995. An Introduction and Presentation of the Material. Eastern connections. Excavations in the black earth 1990-1995. P. 2, Numismatics and metrology | 2004 | 9 | 21 |
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Community detection
Community detection here produces several independent descriptions of how the graph divides, not a single answer to be triangulated (see “Core methodological stance” above). Louvain and Leiden ask “which groups of nodes are more densely interconnected than a random graph with the same degree sequence would predict.” Girvan-Newman asks “which edges, if removed, disconnect otherwise-separate parts of the network.” These are genuinely different questions; neither validates the other.
References:
- Blondel et al. (2008). Fast unfolding of communities in large networks. Journal of Statistical Mechanics, P10008.
- Traag et al. (2019). From Louvain to Leiden. Scientific Reports, 9, 5233.
- Girvan & Newman (2002). Community structure in social and biological networks. PNAS, 99(12), 7821–7826.
- Newman (2006). Modularity and community structure in networks. PNAS, 103(23), 8577–8582.
Louvain communities: 28 Modularity: 0.6708 | community | size |
|---|---|
| 3 | 1338 |
| 2 | 1252 |
| 1 | 1203 |
| 28 | 1109 |
| 14 | 941 |
| 17 | 870 |
| 7 | 831 |
| 10 | 727 |
| 8 | 574 |
| 12 | 503 |
| 24 | 442 |
| 4 | 427 |
| 22 | 379 |
| 15 | 356 |
| 23 | 322 |
| 6 | 317 |
| 20 | 314 |
| 25 | 312 |
| 18 | 311 |
| 11 | 282 |
Leiden communities: 31 Modularity: 0.6971 | community | size |
|---|---|
| 2 | 1215 |
| 31 | 1119 |
| 6 | 934 |
| 3 | 926 |
| 13 | 832 |
| 23 | 823 |
| 21 | 755 |
| 14 | 660 |
| 8 | 581 |
| 5 | 550 |
| 9 | 519 |
| 20 | 500 |
| 15 | 458 |
| 28 | 448 |
| 11 | 365 |
| 30 | 352 |
| 24 | 339 |
| 7 | 328 |
| 25 | 307 |
| 17 | 297 |
K-means clustering
K-means clusters nodes based on their centrality feature profiles rather than graph structure. It groups works that occupy similar structural positions — for example, highly-cited authorities vs. high-betweenness brokers vs. peripheral works — rather than groups that densely cite each other. This is a further independent description, not a validation of the community-detection methods above.
Cluster sizes:
1 2 3 4 5 6
7299 8 6227 746 1 50 