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 ...
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 degre ...
follows a
power law
In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities: one qua ...
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
Assortativity, or assortative mixing is a preference for a network's nodes to attach to others that are similar in some way. Though the specific measure of similarity may vary, network theorists often examine assortativity in terms of a node's de ...
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 co ...
. 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