AUTHOR=Prettejohn Brenton J., Berryman Matthew J., McDonnell Mark D. TITLE=Methods for Generating Complex Networks with Selected Structural Properties for Simulations: A Review and Tutorial for Neuroscientists JOURNAL=Frontiers in Computational Neuroscience VOLUME=5 YEAR=2011 URL=https://www.frontiersin.org/journals/computational-neuroscience/articles/10.3389/fncom.2011.00011 DOI=10.3389/fncom.2011.00011 ISSN=1662-5188 ABSTRACT=

Many simulations of networks in computational neuroscience assume completely homogenous random networks of the Erdös–Rényi type, or regular networks, despite it being recognized for some time that anatomical brain networks are more complex in their connectivity and can, for example, exhibit the “scale-free” and “small-world” properties. We review the most well known algorithms for constructing networks with given non-homogeneous statistical properties and provide simple pseudo-code for reproducing such networks in software simulations. We also review some useful mathematical results and approximations associated with the statistics that describe these network models, including degree distribution, average path length, and clustering coefficient. We demonstrate how such results can be used as partial verification and validation of implementations. Finally, we discuss a sometimes overlooked modeling choice that can be crucially important for the properties of simulated networks: that of network directedness. The most well known network algorithms produce undirected networks, and we emphasize this point by highlighting how simple adaptations can instead produce directed networks.