Inheritance Patterns in Citation Networks Reveal Scientific Memes

Memes are the cultural equivalent of genes that spread across human culture by means of imitation. What makes a meme and what distinguishes it from other forms of information, however, is still poorly understood. Our analysis of memes in the scientific literature reveals that they are governed by a surprisingly simple relationship between frequency of occurrence and the degree to which they propagate along the citation graph. We propose a simple formalization of this pattern and validate it with data from close to 50 million publication records from the Web of Science, PubMed Central, and the American Physical Society. Evaluations relying on human annotators, citation network randomizations, and comparisons with several alternative approaches confirm that our formula is accurate and effective, without a dependence on linguistic or ontological knowledge and without the application of arbitrary thresholds or filters.

Popular Summary

It is widely known that certain cultural entities—known as “memes”—in a sense behave and evolve like genes, replicating by means of human imitation. A new scientific concept, for example, spreads and mutates when other scientists start using and refining the concept and cite it in their publications. Unlike genes, however, little is known about the characteristic properties of memes and their specific effects, despite their central importance in science and human culture in general. We show that memes in the form of words and phrases in scientific publications can be characterized and identified by a simple mathematical regularity.

We define a scientific meme as a short unit of text that is replicated in citing publications (“graphene” and “self-organized criticality” are two examples). We employ nearly 50 million digital publication records from the American Physical Society, PubMed Central, and the Web of Science in our analysis. To identify and characterize scientific memes, we define a meme score that consists of a propagation score—quantifying the degree to which a meme aligns with the citation graph—multiplied by the frequency of occurrence of the word or phrase. Our method does not require arbitrary thresholds or filters and does not depend on any linguistic or ontological knowledge. We show that the results of the meme score are consistent with expert opinion and align well with the scientific concepts described on Wikipedia. The top-ranking memes, furthermore, have interesting bursty time dynamics, illustrating that memes are continuously developing, propagating, and, in a sense, fighting for the attention of scientists.

Our results open up future research directions for studying memes in a comprehensive fashion, which could lead to new insights in fields as disparate as cultural evolution, innovation, information diffusion, and social media.

Figure 1

Citation networks of the Web of Science and the American Physical Society (APS) data sets reveal community structures that nicely align with scientific disciplines, journals covering particular subfields, and occurrences of memes. The generation of the visualizations is based on Gephi [31] and the OpenOrd plug-in [30], which implements a force-directed layout algorithm that is able to handle very large graphs.

Figure 2

Universality in the distribution patterns of scientific memes across data sets. Heat maps encode the density of all $n$-grams with $M\ne 0$ ($N$ being the number of such $n$-grams) with respect to their propagation score and frequency. Panels (a), (c), and (d) each show a broad band with a downward slope for the data sets from the APS, the open access subset of PubMed Central, and the Web of Science, respectively. The 99.9% quantile with respect to the meme score distribution ($M_{0.999}$) is depicted as a white line. Memes are located mostly around the very edge of the top right-hand side of the band (in the vicinity of the 99.9% quantile line). Panel (b) shows the results obtained with a time-preserving randomization of the APS citation graph (see Sec. 4 for details).

Figure 3

The meme score outperforms alternative metrics. The box plot shows the agreement with the ground-truth list of physics terms extracted from Wikipedia as achieved by the different metrics. Agreement is measured as the area under the curve $A$, as shown for the meme score in the embedded graph on the top right. The curves are defined as the percentage from the $x$ top-ranked terms that also appear on the ground-truth list for the different parameter settings ($1\le \delta \le 10$ for the meme score; the thick line stands for $\delta =4$, which has the largest area $A$; see Sec. 4 for details).

Figure 4

Panel (a) shows that phrases with a high meme score (i.e., around the 99.9% quantile $M_{0.999}$) tend to be found as titles of Wikipedia articles on physics, while other phrases tend not to. Panel (b) shows that phrases of relatively low frequency but high meme score have the highest density of terms containing chemical formulas (e.g., ${\mathrm{MgB}}_2$). The data points of the two plots are the same as in Fig. 2, except for the colors showing the relative density of the specific type of terms. Note that the colors are log scaled: white stands for 100% terms of the given type, yellow for $\approx 30\%$, orange for $\approx 10\%$, light red for $\approx 2\%$, dark red for $<1\%$, and black for $<0.1\%$.

Figure 5

Time history of top physics memes based on their meme scores obtained from the American Physical Society data set. The time axis is scaled by publication count. Bars and labels are shown for all memes that top the rankings for at least 10 out of the displayed 911 points in time. The gray area represents the second-ranked meme at a given time.