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Figure 4
Motif contributions to average correlations in random networks.
Top: low connectivity, 
. Bottom: higher connectivity, 
. Other parameters as in Figure 2. A: Spectra of connectivity matrices (fixed out-degree), eigenvalues in the complex plane. Red circle: theoretical radius for bulk spectrum. Red cross: mean input to a neuron. The networks are inhibition dominated (
) and real parts of all eigenvalues are below one (dashed line). B: Contributions of different motifs to average correlation. Comparison between theoretical prediction, random networks with uniform connection probabilities (average across 10 realisations, error bars indicate standard deviation), and networks with fixed out-degree. While in the sparse network only the first few orders contribute, higher orders contribute significantly in the dense network. The analytical expression for the average correlation reproduces the values for networks with fixed out-degrees and approximates the values for random networks. Within one order, chain motifs hardly add to correlations, while common input motifs have a larger contribution. Since inhibition dominates in the network, contributions are positive for even orders 
and negative for uneven orders. Refer to Figure 3 for the correspondence of symbols and paths.
doi: https://doi.org/10.1371/journal.pcbi.1002059.g004