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One-point correlations are the correlations between indegree and outdegree of a node of a directed network. Nodes with large indegree are hubs, nodes with large outdegree are authorities. To calculate the correlation between indegree and outdegree is a way to check whether hubs are also authorities or not.

Pros & Cons

The network to analyze must be directed, otherwise there are no special constraints.


Useful in many contexts. As an example, for the World Wide Web, the study of one-point correlations allows to address the question: are the most linked URLs also the ones that link more pages?

Implementation Details

The algorithm was implemented and documented by S. Fortunato, integrated by S. Fortunato and W. Huang.


Albert, R., and Barabasi, A.-L. (2002) Statistical mechanics of complex networks. Review of Modern Physics 74:47-97.

Newman, M.E.J. (2003) The structure and function of complex networks. SIAM Review 45:167-256.

Pastor-Satorras, R., Vespignani, A.(2002) Evolution and Structure of the Internet. Cambridge University Press.

Boccaletti, S., Latora, V., Moreno, Y.,Chavez, M., Hwang, D.-U.(2006) Complex networks: Structure and dynamics. Physics Reports 424: 175-308.

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