Empirical analysis of the evolution of a scientific collaboration network

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Abstract

We present an analysis of the temporal evolution of a scientific coauthorship network, the genetic programming network. We find evidence that the network grows according to preferential attachment, with a slightly sublinear rate. We empirically find how a giant component forms and develops, and we characterize the network by several other time-varying quantities: the mean degree, the clustering coefficient, the average path length, and the degree distribution. We find that the first three statistics increase over time in the growing network; the degree distribution tends to stabilize toward an exponentially truncated power-law. We finally suggest an effective network interpretation that takes into account the aging of collaboration relationships.

Section snippets

Introduction and previous work

In recent years, thanks to the increasing availability of machine-readable data, many large networks have been empirically analyzed in detail in several disciplines including communications and information networks, biological, social, and technological networks. In many cases it has been found that these networks have small diameters and high clustering. In other words, any node is relatively close to any other node, and the local connection structure will not be random, but rather shaped by

The frozen collaboration network in 2006

We treat the GP social network as a graph where each node is a GP researcher, i.e. someone who has at least one entry in the bibliography. There is a connection between two people if they have coauthored one or more papers, or if they have coedited at least one book or proceeding. In order to characterize the strength of the interaction, one could attribute a weight wij to a link ij with a value proportional, say, to the number of papers coauthored by i and j. However, in the following

Network evolution

In this section we investigate the time evolution of several interesting aspects of the collaboration network.

Testing for preferential attachment

In this section the data is used to test whether the preferential attachment hypothesis (see Section 1) during network growth can be confirmed. As stated in the introduction, preferential attachment has been empirically found in the evolution of several network types, including scientific collaboration networks [3], [4], [5], [10]. However, there are some differences as for the functional form of the effect. In some cases it appears to be quite close to linear, while in other cases it has been

An effective network?

The analysis presented above as well as those of Refs. [3], [4], [5], [10] assume that, once a collaboration between two researchers has been established (a reference to another page in the Wikipedia case), it stays there forever. This seems to be a safe first approximation as scientists remain active for quite a long time in general, at least for the time windows used in Refs. [3], [4], [5]. However, when one looks closely at how these collaborations are established and maintained, one sees

Conclusions

In this work we have studied the temporal evolution of a collaboration network among researchers in the genetic programming field. The distinguishing feature with respect to other similar investigations is that, thanks to the availability of data, we were able to study the network growth from the very beginning and over a 20-year period, which is particularly helpful to watch the formation of the giant component, a process that appears to be still incomplete in the present case. Moreover, the

Acknowledgments

We would like to thank W. B. Langdon, who kindly made the data used in this study available to us. We also thank an anonymous reviewer for his useful comments on the manuscript.

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