Spectral coarse graining and rescaling for preserving structural and dynamical properties in graphs
M Schmidt1, F Caccioli1, T Aste1
1University College London, Department of Computer Science, United Kingdom.
None:
We introduce a graph renormalization procedure based on the coarse-grained Laplacian, which generates reduced-complexity representations across scales. This method retains both dynamics and large-scale topological structures, while reducing redundant information, facilitating the analysis of large graphs by decreasing the number of vertices. Applied to graphs derived from electroencephalogram recordings of human brain activity, our approach reveals collective behavior emerging from neuronal interactions, such as coordinated neuronal activity. Additionally, it shows dynamic reorganization of brain activity across scales, with more generalized patterns during rest and more specialized and scale-invariant activity in the occipital lobe during attention.
More Related Videos
Related Concept Videos
Graphical and Analytic Representation of Sinusoids
The first step is measuring the peak-to-peak value, which is twice the amplitude of the sinusoid. This provides information about the maximum voltage swing of the waveform.
Secondly, the period and angular frequency are determined. The period is the time taken for one complete cycle of the waveform, while...
Shape and Texture of Coarse Aggregate
Three-Dimensional Analysis of Strain
Scaling
Downsampling
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...
Stability of structures


