Higher Order Networks An Introduction To Simplicial Complexes
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Higher Order Networks: An Introduction to Simplicial Complexes
Author: Ginestra Bianconi
language: en
Publisher: Cambridge University Press
Release Date: 2021-12-23
This Element presents one of the most recent developments in network science in a highly accessible style. This Element will be of interest to interdisciplinary scientists working in network science, in addition to mathematicians working in discrete topology and geometry and physicists working in quantum gravity.
Higher-Order Systems
Author: Federico Battiston
language: en
Publisher: Springer Nature
Release Date: 2022-04-26
The book discusses the potential of higher-order interactions to model real-world relational systems. Over the last decade, networks have emerged as the paradigmatic framework to model complex systems. Yet, as simple collections of nodes and links, they are intrinsically limited to pairwise interactions, limiting our ability to describe, understand, and predict complex phenomena which arise from higher-order interactions. Here we introduce the new modeling framework of higher-order systems, where hypergraphs and simplicial complexes are used to describe complex patterns of interactions among any number of agents. This book is intended both as a first introduction and an overview of the state of the art of this rapidly emerging field, serving as a reference for network scientists interested in better modeling the interconnected world we live in.
The Science of Influencers and Superspreaders
This book explores the identification of influencers in complex networks, bridging theoretical approaches with practical applications across diverse fields. It examines interdisciplinary complex systems, including online social media, biological networks, brain networks, socioeconomic and financial systems, and ecosystems. The research presented aims to benefit scientists in relevant areas and inspire new scientific inquiries, potentially advancing the field of influencer identification. In this context, 'influencer' serves as an umbrella term for essential, core, or central nodes within any complex network. The book investigates various manifestations of influencers, such as key figures in social media, critical nodes in genetic and brain networks, keystone species in ecosystems, systemically important banks in financial markets, and disease superspreaders. These diverse scenarios are approached by mapping the influencer identification problem to challenges in physics or computer science. The book caters to readers at three distinct levels: 1. Those seeking mathematically rigorous theories of influencers will find Chapter 2 particularly valuable, as it delves into the mathematical foundations of influencer identification algorithms. Subsequent chapters explore the application of these theories across various disciplines. 2. Data scientists interested in implementing these algorithms in their research and practical work will find relevant information throughout the book. 3. Professionals in finance, marketing, politics, and social media, as well as readers curious about the intersection of big data, influencers, and AI, will gain insights into how these tools can enhance decision-making processes. These readers are encouraged to focus on the introduction and chapters most relevant to their fields, while briefly reviewing the more technical sections. By offering this multi-layered approach, the book aims to provide a comprehensive understanding of influencer identification in complex networks, from theoretical foundations to real-world applications across various domains.