electronics Article Visibility Graph Analysis of IOTA and IoTeX Price Series: An Intentional Risk-Based Strategy to Use 5G for IoT Alberto Partida 1, * ,† , Regino Criado 2,† and Miguel Romance 2,†   Citation: Partida, A.; Criado, R.; Romance, M. Visibility Graph Analysis of IOTA and IoTeX Price Series: An Intentional Risk-Based Strategy to Use 5G for IoT. Electronics 2021, 10, 2282. https://doi.org/ 10.3390/electronics10182282 Academic Editor: Avishek Nag Received: 31 July 2021 Accepted: 4 September 2021 Published: 17 September 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 International Doctoral School, Rey Juan Carlos University, 28933 Madrid, Spain 2 Department of Applied Mathematics, Rey Juan Carlos University, 28933 Madrid, Spain; regino.criado@urjc.es (R.C.); miguel.romance@urjc.es (M.R.) * Correspondence: apartidar@gmail.com † Current address: Móstoles Campus, Rey Juan Carlos University, 28933 Madrid, Spain. Abstract: The transformation of time series into complex networks through visibility graphs is an innovative way to study time-based events. In this work, we use visibility graphs to transform IOTA and IoTeX price volatility time series into complex networks. Our aim is twofold: first, to better understand the markets of the two most capitalised Internet of Things (IoT) platforms at the time of writing. IOTA runs on a public directed acyclic graph (DAG) and IoTeX on a blockchain. Second, to suggest how 5G can improve information security in these two key IoT platforms. The analysis of the networks created by the natural and horizontal visibility graphs shows, first, that both IOTA and IoTeX are still at their infancy in their development, with IoTex seemingly developing faster. Second, both IoT tokens form communities in a hierarchical structure, and third, 5G can accelerate their development. We use intentional risk management as a lever to understand the impact of 5G on IOTA and IoTeX. Our results lead us to provide a set of design recommendations that contribute to improving information security in future 5G-based IoT implementations. Keywords: IoT; IOTA; IoTeX; blockchain; decentralised ledger; cryptocurrencies; complex networks; visibility graph; powerlaw; data integrity; intentional risk; resilience 1. Introduction 1.1. Foundations of This Study: From Time Series to Complex Networks In mathematics, a time series is a succession of events ordered by time. Time series analysis aims to describe the statistical characteristics of the data. Time series forecasting aims to use a model to predict future values [1]. Network science is a scientific discipline at the crossroad of mathematics, statistics and physics [2]. It characterises systems composed of a collection of nodes and edges between them. They constitute a network. The nodes represent the members of the system and the edges certain relations or transfers between them. When the number of nodes and edges is high, i.e., thousands to millions, these systems create a complex network. Complex network analysis provides insights into how these systems grow, evolve and interact with their members. It is possible to transform a time series into a complex network thanks to an easy-to-implement algorithm, i.e., a visibility graph [3]. This conversion facilitates the study of the system whose events create a time series with the powerful analysis toolkit that complex network science provides. In our case, we transform the time series created from the daily prices of the two most capitalised Internet of Things (IoT) tokens into their corresponding complex networks. These visibility networks help us understand how these two IoT platforms behave and grow: IOTA and IoTeX, the former implemented on a directed acyclic graph (DAG) and the latter on a blockchain. We apply our findings to a real life scenario, i.e., the deployment of 5G mobile networks, and we use concepts stemming from intentional risk management to suggest specific 5G design choices that can potentially improve the resilience against intentional risk of both IoT platforms. Electronics 2021, 10, 2282. https://doi.org/10.3390/electronics10182282 https://www.mdpi.com/journal/electronics