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KONECT > Plots > Top-k eigenvalues

Top-k Eigenvalues

The eigenvalues of a network's characteristic matrices \(\mathbf A\), \(\mathbf N\) and \(\mathbf L\) are often used to characterize the network as a whole. KONECT supports computing and visualizing the spectrum (i.e., the set of eigenvalues) of a network in multiple ways. Two types of plots are supported: Those showing the top-\(k\) eigenvalues computed exactly, and those showing the overall distribution of eigenvalues, computed approximately. The eigenvalues of \(\mathbf A\) are positive and negative reals, the eigenvalues of \(\mathbf N\) are in the range \([-1,+1]\), and the eigenvalues of \(\mathbf L\) are all nonnegative. For \(\mathbf A\) and \(\mathbf N\), the largest absolute eigenvalues are used, while for \(\mathbf L\) the smallest eigenvalues are used.

Top-k eigenvalues of A

Top-k eigenvalues of N

Top-k eigenvalues of L