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Figure 2 | EPJ Data Science

Figure 2

From: Reciprocity and impact in academic careers

Figure 2

Illustration of the geodesic distance 1 null network model. Randomly selected pairs of links representing citations between papers are swapped with probability \(1/2\) whenever they fulfil two conditions on time and “distance” (see Methods). Panels in the Figure illustrate the main ingredients and steps of the null model. (a) Two randomly selected pairs of citations \(p_{1} \rightarrow p_{2}\) and \(p_{3} \rightarrow p_{4}\) between papers \(p_{j}\) \((1 \leq j \leq 4)\). We highlight two authors \(a_{1}\) and \(a_{2}\) in orange and blue respectively, to draw attention to the aforementioned “distance” constraint, i.e., that links are rewired only when the papers they connect either share at least one common author, or there exists at least one citation between authors from the two papers in the author citation network (see Methods). (b) The citation network of authors constructed from the papers in (a), where we highlight authors \(a_{1}\) and \(a_{2}\) and the presence of a pair of reciprocated citations between them. (c) Citation-based indicators and statistics of authors in the network. (d) Rewiring of the links, which leads to two new citations \(p_{1} \rightarrow p_{4}\) and \(p_{2} \rightarrow p_{3}\). (e) The citation network of authors constructed from (d) after removing self-citations. (f) Citation-based indicators and statistics of authors after the rewiring. As it can be seen, it follows from our rewiring method that the number of citations received and the h-index of all authors are preserved

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