Analogy To Fourier Analysis
The Fourier analysis of a function can be seen as a rewriting of the function in terms of harmonic functions instead of pairs. This transformation changes the point of view from time domain to frequency domain and enables many interesting applications in signal analysis, data compression, and filtering. Similarly, Power Graph Analysis is a rewriting or decomposition of a network using bicliques, cliques and stars as primitive elements (just as harmonic functions for Fourier analysis). It can be used to analyze, compress and filter networks. There are, however, several key differences. First, in Fourier analysis the two spaces (time and frequency domains) are the same function space - but stricto sensu, power graphs are not graphs. Second, there is not a unique power graph representing a given graph. Yet a very interesting class of power graphs are minimal power graphs which have the least number of power edges and power nodes necessary to represent a given graph.
Read more about this topic: Power Graph Analysis
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“The whole of natural theology ... resolves itself into one simple, though somewhat ambiguous proposition, That the cause or causes of order in the universe probably bear some remote analogy to human intelligence.”
—David Hume (1711–1776)
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