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% part08_networks.tex — Part VIII, Scientific Knowledge Networks (Agent L/I, 2026-11-03). |
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% Every corpus number is a macro from tables/numbers.tex or appears in a generated table (tables/make_tables.py). |
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−% Result files: results/bibliometrics/*.csv (corpus v2, 2026-11-03 18:0x) and results/graph/cited_age_yearly.csv (v1, pending v2). |
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+% Result files: results/bibliometrics/*.csv (corpus v2, 2026-11-03 18:0x) and results/graph/*.csv (corpus v3 graph, 2026-11-03 18:44; |
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+% tables tab_field_flows, tab_reference_coverage, tab_cited_age regenerated from them by tables/make_tables.py, Agent L/M). |
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\section{Scope and reading rules} |
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\label{sec:net-scope} |
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OpenAlex-primary-field and arXiv \texttt{cs} works after the exclusions of the PRISMA flow, and the indicators |
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inherit the boundary decisions and the affiliation completeness of that corpus. Second, the two periods of the |
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protocol are unequal in length and in completeness: the baseline runs from January 2018 to the end of |
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−November 2022, the post period from December 2022 to the snapshot of October 2026 completed by the API |
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−increment, and the last year of the post period is partial for the reasons set out in |
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+November 2022, the post period from December 2022 to the snapshot of October 2026 (the API increment of |
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+Part~III is archived but not yet merged into the analytical corpus), and the last year of the post period is partial for the reasons set out in |
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Section~\ref{sec:data-dates}. Tables by year therefore carry 2026 as an incomplete row, and the fixed-window |
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citation statistics of Section~\ref{sec:net-citations} are complete only up to the publication years flagged in |
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Table~\ref{tab:citation_windows}. Third, the comparison of periods is descriptive. The protocol states the |
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citing population produces: each publication year is cited by the following two years' output, and that output |
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grows, so later cohorts receive more citations at equal exposure \citep{bornmann2015growth}. The reversal in |
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2023 is the first sign of right truncation in the window, since the third calendar year of the 2023 cohort |
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−is 2025, for which the increment of Part~III is complete but the slower channels of indexing are not; it is |
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+is 2025, for which the slower channels of indexing (and citation extraction) are not complete; it is |
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flagged in the table and is the reason the 2024 row, whose window is formally incomplete, is not used. |
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The Gini coefficient of $c^{(36)}$ is the inequality statistic named, with a deviation in window length |
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defines two levels at which flows are measured: between the taxonomy categories of this study, through the |
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flow matrices of equation~\eqref{eq:flow}, and between the corpus and the rest of the literature, through the |
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external edge set of Section~\ref{sec:m-citgraph}, whose cited works are typed by their OpenAlex field. Only |
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−the second level is available at the time of writing, and only from the first version of the corpus: the |
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−graph tables of \texttt{results/graph/} are being regenerated for corpus v2, and the field-flow file was not |
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−present when this part was written. Figure~\ref{fig:field_inflows}, generated from the v1 file, is |
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−described here qualitatively, and every quantitative statement about it is \pending{v2 graph}. |
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+the second level is available at the time of writing. Figure~\ref{fig:field_inflows} and |
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+Table~\ref{tab:field_flows} are generated from the current graph tables of \texttt{results/graph/} |
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+(\texttt{field\_flows\_yearly.csv}, corpus v3), and Table~\ref{tab:reference_coverage}, from |
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+\texttt{reference\_coverage\_yearly.csv}, gives the denominators on which every share in this section rests: |
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+the declared references of the eligible works of each citing year, the share of them that resolve to an |
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+OpenAlex record, and the split of the resolved references into internal and external edges. |
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\begin{figure}[htbp] |
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\centering |
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\includegraphics[width=0.95\textwidth]{fig_field_inflows.pdf} |
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\caption{Share of the resolved references of eligible works, by citing year, that point to works inside the |
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−corpus and to works outside it by cited OpenAlex field (seven largest external fields). Generated from the |
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−corpus v1 file \texttt{results/graph/field\_flows\_yearly.csv}; to be regenerated for v2.} |
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+corpus and to works outside it by cited OpenAlex field (seven largest external fields). Generated by |
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+\texttt{figures/make\_figures.py} from \texttt{results/graph/field\_flows\_yearly.csv} (corpus v3); the |
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+values are in Table~\ref{tab:field_flows}.} |
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\label{fig:field_inflows} |
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\end{figure} |
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−The figure separates the references of each citing year into those that point inside the corpus, that is, to |
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−computer-science works published from 2018 onward, and those that point outside it, by the cited work's |
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−field. Its dominant feature is mechanical and must be read first: the share of references pointing inside the |
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−corpus rises steeply with the citing year, and the share pointing to computer science outside the corpus |
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−falls by the same amount, because the corpus starts in 2018 and a work published in 2018 cannot cite inside |
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−it except at age zero, whereas a work published in 2026 has eight years of corpus to cite. The two |
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−computer-science curves together are approximately flat, and their sum is the share of references that |
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−stay within the field. The curves of the other fields are what the flow question is about, and they are |
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−nearly flat over the window: engineering is the largest external field and declines slowly, the social |
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−sciences, mathematics, medicine, psychology and decision sciences each hold a few per cent of references |
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−with no visible change of direction in the post period, and medicine is the only external field whose share |
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−rises slightly at the end of the window. On the v1 evidence the field-level version of H4 is not supported: |
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−the boundary-crossing share of computer-science references toward other OpenAlex fields does not rise |
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−after 2022, and the slow decline of the engineering share continues a trend visible in the baseline. |
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− |
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−This is a weaker statement than the one H4 makes, and the difference should be kept in view. The |
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−hypothesis concerns boundaries \emph{within} computer science (systems toward AI, security toward AI, |
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−human--computer interaction toward AI), and a field whose sub-areas converge on a common set of methods |
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−may well cite less outside the field, not more, as its internal frontier absorbs the attention that used to |
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−go to mathematics or engineering. The flat external shares are therefore compatible with H4 and with its |
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−negation, and only the category flow matrices can decide between them. What the field-level curves do |
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−establish is a boundary condition for the interdisciplinarity literature: the diversity indices of |
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−Section~\ref{sec:m-diversity}, whether Rao--Stirling or Leinster--Cobbold, will be computed over a reference |
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−distribution whose external component is small and stable, so that any change they detect will come from |
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−the internal component. \citet{porter2009interdisciplinarity} found, for six fields over three decades, that |
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−interdisciplinarity measured on references rose slowly and mostly through neighbouring fields; the |
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−computer-science curves are consistent with that pattern and do not show the acceleration that the |
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−foundation-model narrative would predict. |
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+Table~\ref{tab:reference_coverage} is read first because it conditions the rest. The number of declared |
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+references per eligible work rises through the baseline and falls again in the last three citing years, the |
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+2026 row being the shortest; this is the right-truncation of reference lists (recent records are indexed |
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+before their reference lists are complete) rather than a change in citing practice, and it means that the |
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+shares of the last two rows of every table in this section are computed on fewer references per work than |
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+the earlier rows. The share of declared references that resolve to an OpenAlex record is nearly constant |
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+from 2018 to 2024 and higher in 2025--2026; the recent cohorts carry fewer parsed references per work (the |
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+reference-extraction channels of OpenAlex lag publication), and the references that are already parsed for |
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+them resolve more often. The difference describes how the database was assembled, not what authors cite, and |
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+it is the reason the flow statistics are expressed as shares of resolved references, as the methodology requires. |
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+The internal share of resolved references rises steeply with the citing year, and this is the mechanical |
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+feature of Figure~\ref{fig:field_inflows} that must be read before any other: the corpus starts in 2018, so a |
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+work published in 2018 cannot cite inside it except at age zero, whereas a work published in 2026 has eight |
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+years of corpus to cite. The share of references pointing to computer science outside the corpus, which is |
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+mostly pre-2018 computer science, falls as the internal share rises. |
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+ |
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+The two computer-science columns of Table~\ref{tab:field_flows} do not, however, sum to a constant. Their |
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+sum, the share of references that stay within the field, rises in every citing year of the window, and its |
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+complement, the share of references that cross into another OpenAlex field (column `Other fields'), falls in |
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+every year, in the baseline years as in the post years and at a comparable pace on either side of the 2022 |
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+boundary. Engineering, the largest external field, accounts for the greater part of the decline; |
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+mathematics, decision sciences, physics and psychology decline slowly; the social sciences are stable; and |
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+medicine is the only field among the seven whose share rises, so that by the end of the window it is the |
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+second largest external destination after engineering. On this evidence the field-level version of H4 is |
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+not supported: the boundary-crossing share of computer-science references toward other fields does not rise |
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+after 2022, it continues to fall, and no change of pace is visible at the boundary. |
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+ |
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+Two reservations qualify the direction, though not the absence of a break. The first is a classification |
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+boundary. The eligible corpus is the CS core of Part~III, that is, works with a computer-science topic |
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+whatever their primary field, so a post-2018 engineering work with a computer-science topic is an internal |
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+edge while its pre-2018 counterpart is an external edge typed as engineering; as the corpus lengthens, part |
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+of what used to be counted as a flow to engineering or mathematics is re-counted as internal, and the |
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+decline of the external shares is to that extent mechanical. The field-flow file does not type internal |
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+edges by the cited work's primary field, so the size of this effect cannot be removed here; a flow table |
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+that types every resolved reference, internal or external, by primary field would be the correction, and it |
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+is noted for the director. The second is that H4 concerns boundaries \emph{within} computer science |
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+(systems toward AI, security toward AI, human--computer interaction toward AI), and a field whose sub-areas |
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+converge on a common set of methods may well cite less outside the field, not more, as its internal |
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+frontier absorbs the attention that used to go to engineering or mathematics. A falling external share is |
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+therefore compatible with H4 and with its negation, and only the category flow matrices can decide between |
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+them. What the field-level table does establish is a boundary condition for the interdisciplinarity |
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+literature: the diversity indices of Section~\ref{sec:m-diversity}, whether Rao--Stirling or |
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+Leinster--Cobbold, are computed over a reference distribution whose external component is shrinking |
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+smoothly, so that any change they detect at the 2022 boundary will come from the internal component. |
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+\citet{porter2009interdisciplinarity} found, for six fields over three decades, that interdisciplinarity |
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+measured on references rose slowly and mostly through neighbouring fields; the computer-science columns show |
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+the neighbouring fields (engineering, mathematics, decision sciences) losing share and a non-neighbouring |
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+one (medicine) gaining it, and they do not show the acceleration that the foundation-model narrative would |
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+predict. |
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+ |
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+\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3pt}\input{tables/tab_reference_coverage}\endgroup |
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+ |
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+\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{2.5pt}\input{tables/tab_field_flows}\endgroup |
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\subsection{The age of cited work} |
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\label{sec:net-age} |
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become more self-referential and more recent-leaning over the 2010s. |
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Figure~\ref{fig:cited_age} and Table~\ref{tab:cited_age} give the distribution of the age of cited works, the |
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−citing year minus the cited work's publication year, for the resolved references of eligible works. The |
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−cited-age file is the one graph table available at the time of writing, and it is a v1 file; the table will |
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−be regenerated from the v2 file by the same script and its values are \pending{v2 graph}. On the v1 |
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−distribution, the mode of citation age is two years in every citing year, the mean falls monotonically from |
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−2018 to 2025, the median falls from six to five years, the share of references to works at most five years |
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−old rises by more than ten points over the window, and the share to works more than ten years old falls by |
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−about the same amount. The shift is steady and does not accelerate at the 2022 boundary; the post-period |
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−curves in the figure continue the movement of the baseline curves. A small share of references point to |
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+citing year minus the cited work's publication year, for the resolved references of eligible works, read |
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+from the corpus v3 file \texttt{results/graph/cited\_age\_yearly.csv}, which is built on the same edge sets as |
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+Table~\ref{tab:reference_coverage}. The mode of citation age is two years in every citing year (visible in |
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+the figure, where every curve peaks at the same abscissa); the mean age falls in every citing year from 2018 |
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+to 2026; the median falls over the baseline years and is constant from 2021 onward; the share of |
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+references to works at most five years old rises by roughly the amount by which the share of references to |
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+works more than ten years old falls; and the share of references to works at most two years old rises less, |
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+and mostly during the baseline years. The shift is steady and does not accelerate at the 2022 boundary; the |
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+post-period curves in the figure continue the movement of the baseline curves, and the year-to-year changes |
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+of the mean in the table are of the same order before and after it, if anything smaller after. A small share of references point to |
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works dated after the citing work, which arises from preprints cited before their published version carries |
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−a later date and from year-only dates; this share falls over the window as the corpus's own dates become |
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−first-appearance dates, and is excluded from the age statistics. |
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+a later date and from year-only dates; this share falls to zero over the window as the corpus's own dates |
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+become first-appearance dates, and it is excluded from the age statistics. |
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\begin{figure}[htbp] |
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\centering |
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\includegraphics[width=0.95\textwidth]{fig_cited_age.pdf} |
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\caption{Distribution of the age of cited works (citing year minus cited year, 0 to 30 years) for five |
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−citing years. Generated from the corpus v1 file \texttt{results/graph/cited\_age\_yearly.csv}; to be |
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−regenerated for v2.} |
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+citing years. Generated by \texttt{figures/make\_figures.py} from |
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+\texttt{results/graph/cited\_age\_yearly.csv} (corpus v3); summary statistics in Table~\ref{tab:cited_age}.} |
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\label{fig:cited_age} |
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\end{figure} |
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coverage of OpenAlex imposes. If the probability that a reference string resolves to an OpenAlex record is |
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higher for recent, DOI-bearing works than for older ones, as \citet{culbert2025openalexcoverage} report in |
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their comparison with Web of Science and Scopus, then the resolved references are biased toward youth, and a |
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−constant true age distribution would appear to become younger as the resolvable share rises. The reference |
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−coverage table of the methodology (declared, internal and external references by year) is the control for |
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−this and is part of the pending v2 graph; the age shift is reported here as observed, not as corrected. |
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+constant true age distribution would appear to become younger as the resolvable share rises. |
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+Table~\ref{tab:reference_coverage} is the control. The resolved share is nearly constant from 2018 to 2024, |
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+so over those years a resolution bias toward recent works would shift the level of the age distribution but |
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+not its trend; the fall of the mean and of the over-ten-year share between 2018 and 2024 is therefore not an |
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+artefact of a rising resolvable share. The 2025 and 2026 rows are different: their resolved share is higher |
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+and their reference lists shorter (right-truncation), and the small further decline of the mean age in those |
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+two rows should not be read on its own. The age shift is reported here as observed within the resolved |
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+references, not as corrected for the composition of the unresolved ones, which cannot be typed. |
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\begingroup\renewcommand{\small}{\footnotesize}\setlength{\tabcolsep}{3.5pt}\input{tables/tab_cited_age}\endgroup |
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H4 (convergence) is not testable in its stated form, which concerns citation flows between areas of the |
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ontology and the modularity of the area network; those statistics await the classification. Its field-level |
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−counterpart, the share of computer-science references that cross into other OpenAlex fields, is flat over the |
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−window on the v1 graph (Section~\ref{sec:net-flows-fields}), which neither supports nor contradicts the |
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−within-field convergence the hypothesis describes. |
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+counterpart, the share of computer-science references that cross into other OpenAlex fields, falls through |
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+the window with no change of pace at the boundary (Table~\ref{tab:field_flows}, |
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+Section~\ref{sec:net-flows-fields}), part of the fall being a mechanical consequence of the corpus |
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+boundary; it neither supports nor contradicts the within-field convergence the hypothesis describes. |
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|
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H5 (concentration) has two components. The citation-inequality component is stated for AI categories and is |
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pending; its aggregate counterpart gives a Gini of three-year citations that falls through the baseline and |