Relevance of observed properties

> By Matthieu Latapy and Clémence Magnien

Relevance of observed properties

Relevance of observed properties

In practice, most complex networks are not directly available: we know them through a measurement procedure only. Such measurements generally give partial samples, which may moreover be biased. However, one generally assumes that the properties observed on the obtained samples are representative of the ones of the actual network.

In order to evaluate the relevance of this approach, we considered several complex networks of interest and plotted the evolution of the main properties observed on samples as a function of the sample size. See our paper Complex Network Measurements: Estimating the Relevance of Observed Properties.

This gives evidence for cases where the observed properties significantly depend on the sample size, as above: the plot gives the observed average degree as a function of the sample size when we measure the exchanges in a P2P network. It appears clearly that the observed value depends greatly on the sample size, and thus any value observed on a given sample should not be trusted.

In the paper, we identify other cases where the properties may be trusted, and we exhibit new properties for which the observed values seem more reliable than the ones of classical properties.

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