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# Table 4 Inverse participation ratio (IPR)

From: Network spectra for drug-target identification in complex diseases: new guns against old foes

The distribution of eigenvectors components can be used to obtain non-random system dependent information (Fig. 4). The inverse participation ratio (IPR) has long been employed to analyze localization properties of the eigenvectors (Haake and Zyczkowski 1990). For \(E_{l}^{k}\) denoting |

\( I^{k} = \frac { \sum _{l=1}^{N} \left [E_{l}^{k}\right ]^{4}}{ \left (\sum _{l=1}^{N} \left [E_{l}^{k}\right ]^{2}\right)^{2}} \text {(3)} \) |

which shows two limiting values: (i) a vector with identical components \(E_{l}^{k} \equiv 1/\sqrt {N}\) has |

Further, the average IPR in order to measure an overall localization of the network is calculated as (Jalan and et al. 2011), |

\( \langle IPR \rangle = \frac { \sum _{k=1}^{N} \left [I^{k}\right ]}{N} \text {(4)} \) |

Note that IPR defined as above, separates out the top contributing nodes by keeping the threshold as 1/ |