'Structural equivalence' (Lorrain & White, 1971) describes two nodes' identical position within one shared network, not two investigations sharing a method across unconnected referents
François Lorrain and Harrison C. White's foundational social-network-analysis paper gives "structural equivalence" a formal definition: "Objects a, b of a category C are structurally equivalent if, for any morphism M and any object x of C, aMx if and only if bMx, and xMa if and only if xMb... From the point of view of the logic of the structure, then, a and b are absolutely equivalent, they are substitutable." Two nodes can share an identical relational pattern to everything else in a network without ever being tied to each other directly — on its face a candidate for "same relational pattern, no direct connection."
The term has been imported into citation analysis itself. Chen (2019), applying it to a journal-citation network, writes: "Since the seminal works published by Doreian (1985) and Doreian and Fararo (1985), the SNA's structural equivalence approach has been employed to investigate whether journals are equivalent to neighbours, that is, they have exactly the same pattern of sending and receiving citations in a J2J network." Chen also reproduces the definition's core sentence verbatim, page-cited to p. 63 ("In other words, a is structurally equivalent to b if a relates to every object x of C in exactly the same ways as b does"), which the capture re-verified against the original.
The mismatch with the vault's category is structural in the technical sense. Structural equivalence is a property of two nodes inside one shared, already-existing network — here, a citation network where every journal already has ties to every other — and it typically surfaces only after a formal collapse of that network: "In most social networks... no two distinct objects are structurally equivalent. Structural equivalence of nodes usually appears only once a reduction of the morphisms of [the network] has been accomplished." The vault's bridges (observation-brooks-dreyfus-forgetting-bridge-is-method-level-not-mechanism-level) are not two nodes inside one network compared for equivalent position; they are two separate research projects, run on two disconnected citation neighborhoods, that happen to use the same investigative technique. The term is real, older than the vault's synthesis, and citation-analysis-native — and it is still not the vault's category. See observation-vaults-in-between-bridge-category-not-exactly-named-by-located-literature and moc-argument-from-silence; on the broader habit of citation-analysis literature naming a scalar or structural property the vault also circles, compare claim-petiska-2023-chatgpt-cites-by-google-scholar-count-perpetuates-matthew-effect.
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“Objects a, b of a category C are structurally equivalent if, for any morphism M and any object x of C, aMx if and only if bMx, and xMa if and only if xMb. In other words, a is structurally equivalent to b if a relates to every object x of C in exactly the same ways as b does. From the point of view of the logic of the structure, then, a and b are absolutely equivalent, they are substitutable.”
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