Identifying the perceived local properties of networks reconstructed from biased random walks

TL;DR

This study investigates how well local properties of networks can be reconstructed from symbol sequences generated by biased random walks, revealing biases toward high-degree nodes improve reconstruction except for clustering and eccentricity.

Contribution

It demonstrates the influence of agent bias on the accuracy of reconstructing network properties from sequences, highlighting the effectiveness of high-degree node bias.

Findings

Bias toward high-degree neighbors improves reconstruction performance.

Clustering coefficient and eccentricity are less affected by walk bias.

Self-avoiding walks perform similarly to high-degree bias in property recovery.

Abstract

Many real-world systems give rise to a time series of symbols. The elements in a sequence can be generated by agents walking over a networked space so that whenever a node is visited the corresponding symbol is generated. In many situations the underlying network is hidden, and one aims to recover its original structure and/or properties. For example, when analyzing texts, the underlying network structure generating a particular sequence of words is not available. In this paper, we analyze whether one can recover the underlying local properties of networks generating sequences of symbols for different combinations of random walks and network topologies. We found that the reconstruction performance is influenced by the bias of the agent dynamics. When the walker is biased toward high-degree neighbors, the best performance was obtained for most of the network models and properties. Surprisingly, this same effect is not observed for the clustering coefficient and eccentric, even when large sequences are considered. We also found that the true self-avoiding displayed similar performance as the one preferring highly-connected nodes, with the advantage of yielding competitive performance to recover the clustering coefficient. Our results may have implications for the construction and interpretation of networks generated from sequences.