The eigen exponent: E

• Eigenvalues of a graph are closely related to many basic topological properties (diameter, |E|, number of spanning trees, etc.)

• Plot the eigenvalue li versus i in log-log scale

• Again, plot is found to be linear with a high-correlation factor

• Power-Law 3 (eigen exponent): The eigenvalues, li, of a graph are proportional to the order, i, to the power of a constant, E:

  • li is proportional to iE

• Definition: Define the eigen exponent, E, to be the slop of the plot

• Exponent Top1 Top2 Top3 Top4 eigen -0.471 -0.502 -0.487 -0.17

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