Measuring complexity

There is no single definition of complexity (Edmonds 1999; Gershenson 2008; Mitchell 2009; De Domenico, et al., 2019), as it acquires different meanings in different contexts. A general notion is the amount of information required to describe a phenomenon (Prokopenko, et al. 2008) , but it can also be understood as the length of the shortest program required to compute that description, as the time required to compute that description, as the minimal model to statistically de...

The standard assumptions that underlie many conceptual and quantitative frameworks do not hold for many complex physical, biological, and social systems. Complex systems science clarifies when and why such assumptions fail and provides alternative frameworks for understanding the properties of complex systems. This review introduces some of the basic principles of complex systems science, including complexity profiles, the tradeoff between efficiency and adaptability, the nec...

Network theory provides tools which are particularly appropriate for assessing the complex interdependencies that characterise our modern connected world. This article presents an introduction to network theory, in a way that doesn't require a strong mathematical background. We explore how network theory unveils commonalities in the interdependency profiles of various systems, ranging from biological, to social, and artistic domains. Our aim is to enable an intuitive understa...

In the 21st century, many of the crucial scientific and technical issues facing humanity can be understood as problems associated with understanding, modelling, and ultimately controlling complex systems: systems comprised of a large number of non-trivially interacting components whose collective behaviour can be difficult to predict. Information theory, a branch of mathematics historically associated with questions about encoding and decoding messages, has emerged as somethi...

We will review some of the theoretical progresses that have been in the study of complex systems in physics and of their applications to biology.

We discuss the fundamental theoretical framework together with numerous results obtained by the authors and colleagues over an extended period of investigation on the Information Geometric Approach to Chaos (IGAC).

Review article of various complexity measures of networks

This introductory paper is structured in the form of an "interview", where the author answers the following questions: Why did you begin working with complex systems? How would you define complexity? What is your favourite aspect/concept of complexity? In your opinion, what is the most problematic aspect/concept of complexity? How do you see the future of complexity?

The question What is Complexity? has occupied a great deal of time and paper over the last 20 or so years. There are a myriad different perspectives and definitions but still no consensus. In this paper I take a phenomenological approach, identifying several factors that discriminate well between systems that would be consensually agreed to be simple versus others that would be consensually agreed to be complex - biological systems and human languages. I argue that a crucial ...

The concept of complexity appears in virtually all areas of knowledge. Its intuitive meaning shares similarities across fields, but disagreements between its details hinders a general definition, leading to a plethora of proposed measurements. While each might be appropriated to the problems it addresses, the lack of an underlying fundamental principle prevents the development of a unified theory. Here it is shown that the statistics of the amount of symmetry broken by system...