(A) For an example network with 1200 neurons divided to 3 equally sized groups we plot the autocorrelation function averaged over neurons belonging to the same group. G was chosen such that one eigenvalue of M is greater than 1. Independent of the time lag τ the autocorrelations maintain a constant ratio that is equal to the ratio of the components of the eigenvector of M corresponding to the leading eigenvalue. Inset: for 20 example networks we computed the variance of the autocorrelation vector along the three eigenvectors of M and found that the variation in autocorrelation along the leading eigenvector is three orders of magnitude larger than along the other two directions. (B) In this example network M has two eigenvalues greater than 1. The autocorrelations are no longer a constant ratio of each other, indicating that the network maintains two modes of autocorrelation concurrently. Inset: when averaged over 20 networks we see that the variation along the two eigenvectors with eigenvalues greater than 1 is significantly larger than along the third eigenvector. (C) For the two examples networks shown in (A,B) we plotted the trajectory of the autocorrelation vector as a function of the time lag τ, and show that they are confined to in the subspace spanned by the eigenvectors, V
which has eigenvalues greater than 1.