Scientific collaboration network is a

social network A social network is a social structure made up of a set of social actors (such as individuals or organizations), sets of dyadic ties, and other social interactions between actors. The social network perspective provides a set of methods for an ...

where nodes are scientists and links are co-authorships as the latter is one of the most well documented forms of scientific collaboration. It is an undirected,

scale-free network A scale-free network is a network whose degree distribution follows a power law, at least asymptotically. That is, the fraction ''P''(''k'') of nodes in the network having ''k'' connections to other nodes goes for large values of ''k'' as : P(k) ...

where the

degree distribution In the study of graphs and networks, the degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability distribution of these degrees over the whole network. Definition The degree o ...

follows a

power law In statistics, a power law is a Function (mathematics), functional relationship between two quantities, where a Relative change and difference, relative change in one quantity results in a proportional relative change in the other quantity, inde ...

with an exponential cutoff – most authors are sparsely connected while a few authors are intensively connected. The network has an assortative nature – hubs tend to link to other hubs and low-degree nodes tend to link to low-degree nodes. Assortativity is not structural, meaning that it is not a consequence of the degree distribution, but it is generated by some process that governs the network’s evolution.

Study by Mark Newman

A detailed reconstruction of an actual collaboration was made by

Mark Newman Mark Newman is an English-American physicist and Anatol Rapoport Distinguished University Professor of Physics at the University of Michigan, as well as an external faculty member of the Santa Fe Institute. He is known for his fundamental contri ...

. He analyzed the collaboration networks through several large databases in the fields of biology and medicine, physics and computer science in a five-year window (1995-1999). The results showed that these networks form small worlds, in which randomly chosen pairs of scientists are typically separated by only a short path of intermediate acquaintances. They also suggest that the networks are highly clustered, i.e. two scientists are much more likely to have collaborated if they have a third common collaborator than are two scientists chosen randomly from the community.

Prototype of evolving networks

Barabasi et al. studied the collaboration networks in mathematics and neuro-science of an 8-year period (1991-1998) to understand the

topological In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...

and dynamical laws governing

complex networks Complex Networks is an American media and entertainment company for youth culture, based in New York City. It was founded as a bi-monthly magazine, ''Complex'', by fashion designer Marc (Ecko) Milecofsky. Complex Networks reports on popular a ...

. They viewed the collaboration network as a prototype of evolving networks, as it expands by the addition of new nodes (authors) and new links (papers co-authored). The results obtained indicated that the network is scale-free and that its evolution is governed by

preferential attachment A preferential attachment process is any of a class of processes in which some quantity, typically some form of wealth or credit, is distributed among a number of individuals or objects according to how much they already have, so that those who ...

. Moreover, authors concluded that most quantities used to characterize the network are time dependent. For example, the average degree (network's interconnectedness) increases in time. Furthermore, the study showed that the node separation decreases over time, however this trend is believed to be offered by incomplete database and it can be opposite in the full system.

References

{{Reflist, 2 Social networks