Analytical approach to network inference: Investigating degree distribution

TL;DR

This paper provides an analytical framework to understand how false positive and false negative errors affect network degree distribution and offers a method to reconstruct the true degree distribution from biased data.

Contribution

It introduces an analytical formula for the biased degree distribution and a reliable procedure to reconstruct the true degree distribution considering inference errors.

Findings

Derived an explicit formula for biased degree distribution density.

Proposed a method to reconstruct true degree distribution from inferred network.

Validated the approach through simulation studies.

Abstract

When the network is reconstructed, two types of errors can occur: false positive and false negative errors about the presence or absence of links. In this paper, the influence of these two errors on the vertex degree distribution is analytically analysed. Moreover, an analytic formula of the density of the biased vertex degree distribution is found. In the inverse problem, we find a reliable procedure to reconstruct analytically the density of the vertex degree distribution of any network based on the inferred network and estimates for the false positive and false negative errors based on, e.g., simulation studies.