, Volume 10, Issue 3, pp 287–304

The Connection-set Algebra—A Novel Formalism for the Representation of Connectivity Structure in Neuronal Network Models

Original Article

DOI: 10.1007/s12021-012-9146-1

Cite this article as:
Djurfeldt, M. Neuroinform (2012) 10: 287. doi:10.1007/s12021-012-9146-1


The connection-set algebra (CSA) is a novel and general formalism for the description of connectivity in neuronal network models, from small-scale to large-scale structure. The algebra provides operators to form more complex sets of connections from simpler ones and also provides parameterization of such sets. CSA is expressive enough to describe a wide range of connection patterns, including multiple types of random and/or geometrically dependent connectivity, and can serve as a concise notation for network structure in scientific writing. CSA implementations allow for scalable and efficient representation of connectivity in parallel neuronal network simulators and could even allow for avoiding explicit representation of connections in computer memory. The expressiveness of CSA makes prototyping of network structure easy. A C+ + version of the algebra has been implemented and used in a large-scale neuronal network simulation (Djurfeldt et al., IBM J Res Dev 52(1/2):31–42, 2008b) and an implementation in Python has been publicly released.


Modeling Connectivity Neuronal networks Computational neuroscience Software Formalism 

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.School of Computer Science and CommunicationKTHStockholmSweden

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