Complex Networks: a Mini-review
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GENERAL AND APPLIED PHYSICS
Complex Networks: a Mini-review ´ Angelica Sousa da Mata1 Received: 18 May 2020 © Sociedade Brasileira de F´ısica 2020
Abstract Network analysis is a powerful tool that provides us a fruitful framework to describe phenomena related to social, technological, and many other real-world complex systems. In this paper, we present a brief review about complex networks including fundamental quantities, examples of network models, and the essential role of network topology in the investigation of dynamical processes as epidemics, rumor spreading, and synchronization. A quite of advances have been provided in this field, and many other authors also review the main contributions in this area over the years. However, we show an overview from a different perspective. Our aim is to provide basic information to a broad audience and more detailed references for those who would like to learn deeper the topic. Keywords Complex networks · Centrality measures · Models · Dynamical process
1 Introduction The study of complex networks is inspired by empirical analysis of real networks. Indeed, complex networks allow us to understand various real systems, ranging from technological to biological networks [1]. For instance, we need a set of neurons connected by synapses to ensure our ability to read this text; our body is ruled by interactions between thousands of cells; communication infrastructures, such as the Internet, are formed by routers and computer cables and optical fibers; and the society consists of people connected by social relationships such as friendship and familiar or professional collaborations [1–3]. These systems are called complex systems because it is not possible to predict their collective behavior from their individual components. But understanding the mathematical description of these systems makes us capable to predict them and possibly control them. These are some of the great scientific challenges of the present time, since they play a key role in our daily life [4]. Examples include the understanding of the spreading viruses throughout transportation networks that allowed the prediction of the
Ang´elica Sousa da Mata
[email protected] 1
Departamento de F´ısica, Universidade Federal de Lavras, Lavras, MG, 37200-900, Brazil
H1N1 pandemic [5] in 2009 or the new coronavirus in 2019/2020 [6], and the use of mobile call network to find those responsible for the terrorist attack on a train in Madrid in 2004 [7]. Despite of the differences among complex systems found in nature or society, the structures of these networks are much similar to each other, because they are governed by the same principles. Then, we can use the same set of mathematical and computational tools to explore these systems. In general terms, a network is a system that can be represented as a graph, composed by elements called nodes or vertices and a set of connecting links (edges) that represent the interactions among them [8]. In Fig. 1, we show a classic and famous example of a social network that beca
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