Figure 1

Dependence of the spectrum of effective interaction matrices on the temporal parameter $\tau$. We show the two nonzero eigenvalues of effective interaction matrices for a network with two edges connecting three nodes. Dotted curves: Random sequences with replacement. Solid curves: Random sequences without replacement.Reuse & Permissions

Figure 2

The (negative) spectral gap of the aggregate and temporal Laplacian dynamics for four networks. The error bars indicate the standard deviation calculated on the basis of ${10}^3$ realizations of edge sequences. (a) Results for a random temporal graph having $N=500$ nodes and $|E|=19780$ edges. (b) Results for a scale-free temporal network with $N=500$ and $|E|=19990$. We set the parameters of the Barabási-Albert model to $m=m_0=4$. The degree $d$ obeys a power law with exponent $-3$ [29]. (c) Results for human interaction data with $N=104$ and $|E|=782682$ among students, staff, and faculty members at the Massachusetts Institute of Technology. The data were produced by the Reality Mining Project [30]. Although the original network contains 106 subjects, we used the largest connected component containing 104 subjects. (d) Results for the human interaction data during a conference recorded in the SocioPatterns Project [31]. Although the original data have 113 nodes and 20 818 edges, we excluded one node and the link emanating from this node, possessing two edges on it before the analysis. This is because the spectral gap value is very sensitive to such a nearly isolated node. The modified network has $N=112$ and $|E|=20816$.Reuse & Permissions