Co-citations refer to the fact that two references are cited by the third article. Traditionally as long as two references are cited anywhere within the third article, they are considered as co-cited. If the full text of the third article is available, obviously one can narrow down the scope to sections, paragraphs, or sentences.
Citing a reference may serve many purposes and may be motivated by a wide variety of reasons. However, the way a reference has been cited may function similarly to reference an underlying concept.
An instance of a co-citation is a local event. It only involves two references. These local events contribute to the formation of a network of co-cited references. A primary goal of CiteSpace is to analyze such networks so as to identify patterns and trends concerning the structure and dynamics of the underlying scientific literature.
A co-citation connection between references R1 and R2 is depicted in a visualized network based on the similarity between the two references involved. Assume our dataset consists of 10,000 articles. R1 is cited by 100 of the 10,000 articles and R2 is cited by 100 of them. The similarity is computed based on the articles that cited both R1 and R2 out of the two sets of citing articles. Suppose the number of articles that cited both R1 and R2 is 30, divided by the square root of the multiplication of 100 and 100, which is 100, then the similarity, or the weight of the co-citation link, is 0.30. The maximum similarity of 1.00 is achieved when the two 100-article sets overlap completely, whereas the minimum similarity of 0.00 corresponds to the situation of no overlapping citing articles, i.e. R1 and R2 are never co-cited by any of the 10,000 articles. CiteSpace provides several ways to measure the similarity. 
Co-citations can be seen as a special case of co-occurrences, which can include co-occurring words, or co-words, and another types of entities such as co-authors, or author co-citations.

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