Multiplex reconstruction with partial information

TL;DR

This paper introduces a linear-time algorithm for reconstructing multiplex network structures from partial observations, demonstrating high accuracy with limited data on synthetic and real-world networks.

Contribution

The work presents a novel community-based reconstruction algorithm that effectively infers multiplex topology from partial data, with proven efficiency and accuracy.

Findings

Reconstruction accuracy improves rapidly with more partial information.

Heterogeneity and layer similarity influence reconstruction success.

High accuracy achieved with minimal observed data (e.g., 10% yields 70% accuracy).

Abstract

A multiplex is a collection of network layers, each representing a specific type of edges. This appears to be a genuine representation for many real-world systems. However, due to a variety of potential factors, such as limited budget and equipment, or physical impossibility, multiplex data can be difficult to observe directly. Often, only partial information on the layer structure of the system is available, whereas the remaining information is in the form of a single-layer network. In this work, we face the problem of reconstructing the hidden multiplex structure of an aggregated network from partial information. We propose an algorithm that leverages the layer-wise community structure that can be learned from partial observations to reconstruct the ground-truth topology of the unobserved part of the multiplex. The algorithm is characterized by a computational time that grows linearly with the network size. We perform a systematic study of reconstruction problems for both synthetic and real-world multiplex networks. We show that the ability of the proposed method to solve the reconstruction problem is affected by the heterogeneity of the individual layers and the similarity among the layers. On real-world networks, we observe that the accuracy of the reconstruction saturates quickly as the amount of available information increases. In genetic interaction and scientific collaboration multiplexes for example, we find that 10% of ground-truth information yields 70% accuracy, while 30% information allows for more than 90% accuracy.