Tuesday, May 16, 2006

Economics an emerging small world

S. Goyal, M. J. van der Leij & J.L. Moraga-Gonzalez have written a short piece Economics: An Emerging Small World, in the Journal of Political Economy. This looks at the collaborative or social distance between economists from 1970-2000.

The academic economists who publish in journals can be viewed as a network of collaboration. Every publishing economist is a node in this network and two nodes are linked if the authors have published a paper together. Two authors have distance 1 if they have published together, have distance 2 if they have not published together but have a common co-author and so on. All economists who are directly or indirectly linked are said to belong to the same component and the largest group of interconnected economists is the giant component. The distance between any two economists is the length of the shortest link between them – this is infinite if there is no link. The average distance of a connected network (with a path between every pair of nodes) is the clustering coefficient which measures the overlap between the links of different economists. The network of economists exhibits small-world properties if it is very large compared to the number of links, integrated in the sense that a giant component exists covering many economists, if average distances between nodes in the giant component is small with high clustering.

Goyal et al. find that while the number of economists has more than doubled over the period that distances between economists, while already small, have declined dramatically. The reason for this is that economics is spanned by a collection of interlinked stars – economists who write with many other economists most of whom have few co-authors who generally do not write with each other. There are many stars in economics - Joseph Stiglitz - is an example. The stars act as connectors and reduce the distance between different highly clustered parts of economics.

Over a 10 year period most economists have no more than two co-authors which is small but the average number of authors – the degree of the network – has increased. The giant component has grown from 15% of all nodes to over 40% and has become significantly smaller in terms of distances. Clustering has remained high. Given these four properties, economics is an emerging small world.

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