A citation graph (or citation network), in information science and bibliometrics, is a directed graph that describes the citations within a collection of documents.

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Each vertex (or node) in the graph represents a document in the collection, and each edge is directed from one document toward another that it cites (or vice versa depending on the specific implementation).^[1]

Citation graphs have been utilised in various ways, including forms of citation analysis, academic search tools and court judgements. They are predicted to become more relevant and useful in the future as the body of published research grows.

There is no standard format for the citations in bibliographies, and the record linkage of citations can be a time-consuming and complicated process. Furthermore, citation errors can occur at any stage of the publishing process. However, there is a long history of creating citation databases, also known as citation indexes, so there is a lot of information about such problems.

In principle, each document should have a unique publication date and can only refer to earlier documents. This means that an ideal citation graph is not only directed but acyclic; that is, there are no loops in the graph. This is not always the case in practice, since an academic paper goes through several versions in the publishing process. The timing of asynchronous updates to bibliographies may lead to edges that apparently point backward in time. Such "backward" citations seem to constitute less than 1% of the total number of links.^[2]

As citation links are meant to be permanent, the bulk of a citation graph should be static, and only the leading edge of the graph should change. Exceptions might occur when papers are withdrawn from circulation.^[2]

A citation is a reference to a published or unpublished source (not always the original source).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 point 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).^[3] References to single, machine-readable assertions in electronic scientific articles are known as nanopublications, a form of micro attributions.

Citation networks are one kind of social network that has 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 entitled "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."^[4]

There are several other types of network graphs that are closely related to citation networks. The co-citation graph is the graph between documents as nodes, 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.

While citation graphs have had a noticeable impact on several areas of academia, they are likely to become more relevant in the future. As the body of published research grows, more traditional ways of searching for papers will become less effective in narrowing down relevant papers to a particular topic. For example, text-based similarity can only go so far in selecting which papers are relevant to a topic, whereas the addition of citation graphs could make use of giving higher priority to those papers which have a lot of connections to other papers relevant to the topic.

However, developments like this face similar challenges to that of most applications of citation graphs, which is the face that there is no standardized format or way of citing. This makes the construction of these graphs very difficult, since it requires complex software analysis to extract citations from papers. One solution proposed to this problem is to create open databases of citation information in a format which could be used by anyone and easily converted to a different form, for example a citation graph.^[11]

• Collaboration graph, a graph defined by the authors of documents
• Web graph, a citation graph of references from one web page to another in the World Wide Web
• Directed Acyclic Graph, the formal mathematical structure of a well-constructed citation graph
• Legal citation analysis citation analysis in legal contexts