In his call for open citations, Dario Taraborelli hailed the scholarly citation graph (in which the nodes (vertices) are individual academic publications and the links (edges) represent bibliographic citations from one publication to another) as one of humankind’s most important intellectual achievements.
We all understand that the inclusion within our own academic publications of bibliographic references to the works of others is one of the most explicit ways of acknowledging the thoughts, discoveries, achievements and influences of other scholars, and their contributions to our own work. Not only does what we gain from their publications enable us to make intellectual progress, by “standing on the shoulders of giants” as Newton once famously observed , but the influence of these publications extends forward in time across the entire intellectual landscape, like gigantic shadows cast at sunset, whether or not those influenced by these publications have occasion to reference them in their own works.
A bibliographic citation is not only “a conceptual directional link from a citing entity to a cited entity, created by a human performative act of making a citation”, but it is additionally both enduring and retrospective. Enduring, because once made it persists for ever within the global corpus of scholarly literature, and retrospective because (with the exception of occasional contemporaneous citations) the cited publication predates the citing publication.
At the anterior margin of a crawling cell, cellular protrusive extension (for example of a pseudopodium) is achieved by the catalysed polymerization of new filaments of the cytoskeletal protein actin from attachment sites on an existing stationary actin filament network, pushing the cell margin forward . The scholarly citation network (or citation graph, the two terms here being used interchangeably) is similarly dynamic and temporally directional, being extended forward as new works of scholarship are published. Extension of knowledge is achieved by the catalytic inspiration provided by existing academic publications, themselves temporally stationary within the expanding citation network, leading to the publication of new works of scholarship that cite these previous publications and thus extend the citation network further into the future. The citation graph is thus not just an acyclic directed graph, but an acyclic temporally directed graph. Indeed, it is this temporal aspect of the citation network that is one of its most important features.
To use another analogy, the human genealogical tree is inherently multidimensional and difficult to represent pictorially in its entirety, because each new birth brings together the family trees of the child’s two parents. However, unless the parents are seriously promiscuous, the resulting genealogical tree is not impossibly complex. In contrast, the scholarly citation network is much more highly interlinked, since each new publication cites not just two but many preceding (‘parent’) publications, which themselves may beget many other citations.
Visualization of the global scholarly citation graph, or portions of it, is thus inherently difficult, and the important temporal aspect of the graph is the one ignored by almost every method used for visualizing aspects of that graph. Existing methods may take the broad view, showing the links, and the strength of those links, between one scholarly domain and another, thus visualizing the ‘structure of science’. Alternatively, they may take a more detailed view of a small section of the graph, visualize the proximity of individual publications to one another. Often a radial display is chosen for this, that shows in closest proximity those papers directly referenced by the selected publication in the centre, then at a greater radius those papers referenced by the cited papers shown in the inner circle, and so on. Because of the graph’s complexity, such displays quickly looses intelligibility after two citation links.
Among a small number of visualization applications that do not ignore the temporal aspect of the graph is Citeology, a temporally based citation network visualization tool developed some years ago by Justin Matejka and colleagues at the design software company Autodesk . Unfortunately, this innovative software prototype was not central to that company’s mission, development ceased, and the Citeology Java app is no longer available. However, in his last email to me, Justin Matejka kindly offered to help others re-create this application.
There is thus an urgent need for innovative new open-source visualization tools that will clearly and dynamically display portions of the global citation graph, for example the direct and indirect citation connections between any two publications or any two individuals, along the temporal axis of publication date. Developers within the open science community please step forward!
 Isaac Newton, in a 1675 letter to Robert Hooke, wrote “If I have seen further it is by standing on the shoulders of Giants.” https://discover.hsp.org/Record/dc-9792/
 Bruce Alberts et al. (2014). Molecular Biology of the Cell. 6th Edition. Garland Science. Chapter 16, The Cytoskeleton.
 Justin Matejka, Tovi Grossman, George Fitzmaurice (2012). Citeology: Visualizing Paper Genealogy. ACM Extended Abstracts on Human Factors in Computing Systems. https://www.autodesk.com/research/publications/citeology https://d2f99xq7vri1nk.cloudfront.net/CiteologyVideo.mp4