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Egghe & Rousseau once (1990, p. 228) explained "when a document di cites a document dj, we can show this by an arrow going from the node representing di to the document representing dj. In this way the documents from a collection D form a directed graph, which is called a 'citation graph' or 'citation network' ".
Background and history
Citation is a reference to a published or unpublished source (not always the original source). More precisely, a citation is an abbreviated alphanumeric expression embedded in the body of an intellectual work that denotes an entry in the bibliographic references section of the work. Its purpose is to acknowledge the relevance of the works of others to the topic of discussion at the spot where the citation appears.
Generally the combination of both the in-body citation and the bibliographic entry constitutes what is commonly thought of as a citation (whereas bibliographic entries by themselves are not). References to single, machine-readable assertions in electronic scientific articles are known as nanopublications, a form of microattribution.
Citation networks, the principal focus of this study, are one kind of social networks that have been studied quantitatively almost from the moment citation databases first became available. In 1965, Derek J. de Solla Price described the inherent linking characteristic of the Science Citation Index (SCI) in his paper titled "Networks of Scientific Papers". The links between citing and cited papers became dynamic when the SCI began to be published online. In 1973, Henry Small published his work on co-citation analysis which became a self-organizing classification system that led to document clustering experiments and eventually what is called "Research Reviews".
- Citation networks are directed. The links go from one document to the other.
- All edges in the citation networks point backwards in time. In practice, because there are often many dates associated with a document (electronic and paper publication dates, different versions of one document, and so forth) actual citations may go forwards in time. These can be removed or changed if required. In one example based on the first ten years of papers from arXiv, a little under 1% of citation links were found to be in the 'wrong' direction, i.e. from an older to a newer paper when the date encoded in the index number of the document is used.
- Citation networks are acyclic because a paper can cite only existing papers.
- Vertices and edges added to the citation networks are permanent and cannot be removed at a later time. Some exceptions might include when a document is withdrawn from circulation.
- The already formed part of the network is mostly static and only the leading edge of the network changes.
The large majority of a citation network is therefore a type of Directed acyclic graph which has some distinctive properties.
There are several other types of network (graphs) which are closely related to citation networks. Some are derived from the citation network; the co-citation graph is the graph between documents as nodes but now where two documents are connected if they share a common citation (see Co-citation and Bibliographic coupling). Other related networks are formed using other information present in the document. For instance, in a Collaboration graph, known in this context as a co-authorship network, the nodes are the authors of documents, linked if they have co-authored the same document. The link weights between two authors in co-authorship networks can increase over time if they have further collaboration.
- "Science Citation Index: Effectiveness in locating articles in the anaesthetics field: 'Perturbation of ion transport'. British Journal of Anaesthesia, 43: 814, Cawkell, A. E. (1971)". Archived from the original on 2016-03-04. Retrieved 2015-06-05.
- Zhao, Dangzhi; Strotmann, Andreas (2015-02-01). Analysis and Visualization of Citation Networks. Morgan & Claypool Publishers. ISBN 978-1-60845-939-1.
- Structures and Statistics of Citation Networks, Miray Kas
- Clough, James R.; Gollings, Jamie; Loach, Tamar V.; Evans, Tim S. (2015), "Transitive reduction of citation networks", Journal of Complex Networks, 3 (2): 189–203, arXiv:1310.8224, doi:10.1093/comnet/cnu039, S2CID 10228152.