Reconstructing irreducible links in temporal networks: which tool to choose depends on the network size

Abstract

Filtering information in complex networks entails the process of removing interactions explained by a proper null hypothesis and retaining the remaining interactions, which form the backbone network. The reconstructed backbone network depends upon the accuracy and reliability of the available tools, which, in turn, are affected by the specific features of the available dataset. Here, we examine the performance of three approaches for the discovery of backbone networks, in the presence of heterogeneous, time-varying node properties. In addition to the recently proposed evolving activity driven model, we extend two existing approaches (the disparity filter and the temporal fitness model) to tackle time-varying phenomena. Our analysis focuses on the influence of the network size, which was previously shown to be a determining factor for the performance of the evolving activity driven model. Through mathematical and numerical analysis, we propose general guidelines for the use of these three approaches based on the available dataset. For small networks, the evolving temporal fitness model offers a more reasonable trade-off between the number of links assigned to the backbone network and the accuracy of their inference. The main limitation of this methodology lies in its computational cost, which becomes excessively high for large networks. In this case, the evolving activity driven model could be a valid substitute to the evolving temporal fitness model. If one seeks to minimize the number of links inaccurately included in the backbone network at the risk of dismissing many links that could belong to it, then the temporal disparity filter would be the approach-of-choice. Overall, our contribution expands the toolbox of network discovery in the technical literature and should help users in choosing the right network discovery instrument, depending on the problem considered.

Emergence and structure of decentralised trade networks around dark web marketplaces

“…First, we observe that the U2U network, formed by all transactions between pairs of users, has a larger trading volume than DWMs themselves. We then identify stable U2U trading relationships, which represent a subset of persistent pairs in our dataset 31,32 forming the backbone of the U2U network. We find that 137,667 (i.e., 1.7% out of 7.85 million total) pairs are stable, generating a total trading volume of $1.5 billion (i.e., 5% out of $30 billion total volume).…”

Emergence and structure of decentralised trade networks around dark web marketplaces

“…expected from the null model, it is labeled as stable, otherwise as non-stable. The evolving activity-driven model is an appropriate methodology for large temporal networks 32 and it is implemented in the Python 3 pip library TemporalBackbone, 44 where default parameter values have been used. As input parameter, we considered the full network, comprehending transactions from/to DWMs and U2U transactions between users (see Section 4).…”

Identification of patterns for space-time event networks

“…In other words, according to this criterion, two subgraphs are isomorphic if they are topologically equivalent, and the order of their events is identical. We refer to Kobayashi and Génois (2021), Kobayashi et al (2019), Nadini et al (2020a) and Nadini et al (2020b) for insights on the algorithms and their validation. The algorithm that we propose prioritizes some subgraphs related to the spatio-temporal patterns of events, providing information on co-occurrence and shift.…”