The evolution of a citation network topology

Introduction

The statistical mechanics of complex networks has recently received considerable attention in several science communities, including statistical physics, computer science, and information science. The topological properties of large networks are a main focus of these studies. Network topology can be applied to gain insights into the patterns of citation among scientific papers.

Citation networks reveal patterns of influence on the development of new works, papers that play more central roles in the development of a literature, and the extent to which lines of inquiry form an integrated, cumulative body of scholarship.

General characteristics of the Scientometrics citation network

Figure 1 shows the cumulative number of papers and the number of papers published each year during 26 years. The number of papers published each year is relatively constant, so the cummulative number of papers in network increase linearly with time.

Fig. 1: Annual (inset) and cumulative number of papers in Scientometrics (1978-2004).

Ratios of “journal self-citation” and “journal self-cited” are two important indicators in journal evaluation. Both measures show the degree to which a journal has become recognized as the location in which important research is published.

Figure 2 shows a steadily developing linear trend in self-citation in Scientometrics as the journal

has aged.

This rather high figure suggests that the journal has not yet achieved a highly central place in the entire literature cited by the SCI database.

Annual data on the ratio of “journal self-cited” are not available. However, we do have information on the proportion of papers in Scientometrics that have not been cited by papers inother journals.

This trend is shown in figure 3.

Fig.

3: Percentage of papers in Scientometrics not cited in other journals.

One of the most striking features of the Scientometrics inner-citation network is the large number of papers (some 24%, or 411 nodes), that have no directed relations with other papers.

Without considering self-citation, 44. 1% papers have zero in-degree (are never cited) and 42.5% with zero out-degree (never cite another paper in the journal). Additionally, 95. 17% of the papers in our network are not cited more than eight times. The top 4. 83% papers contain more than 33% of all citations.

The evolution of Scientometrics citation network

If a journal is successful as a context for the publication of a cumulative scientific literature, the extent of internal citation should increase over time. Figure 4 shows that this is generally true of Scientometrics.

Fig. 4: Average references to other papers in the 

 journal.

Fig. 5: Mean geodesic distance in the Scientometrics database. The distance is computed on the cumulative data up to each year.

This inherent tendency to cluster is quantified by clustering coefficient[19].

Ci is the ratio between the number Ei of links that actually exist between the neighbors of a selected node i, and the total number ki(ki-1)/2 of possible links between these neighbors.

The clustering coefficient of the graph, which is a measure of the network’s potential modularity,

is the average over all vertices:

The range of C is 0 <= C <= 1

Conclusion :

The input degree and output degree distributions in the Scientometrics citation network both show a scale free distributions. The high-citation “hubs” in the network act to integrate a very large part of all of the literature ever published in the journal into a single component, and create relatively

short path lengths among clustered local specialty literatures, even as the literature increases steadily in size. The emergence of “hubs” that cumulate knowledge and allow efficient search across diverse communities allows increasingly large and increasingly diverse and specialized literatures to remain connected.