Advances in Complex Systems

In many engineered and natural networked systems, there has been great interest in leader selection and/or edge assignment during the optimal design of controllable networks. In this paper, we present our pioneering work in leader–follower network design via memetic algorithms, which focuses on minimizing the number of leaders or the amount of control energy while ensuring network controllability. We consider three problems in this paper: (1) selecting the minimum number of leaders in a pre-defined network with guaranteed network controllability; (2) selecting the leaders in a pre-defined network with the minimum control energy; and (3) assigning edges (interactions) between nodes to form a controllable leader–follower network with the minimum control energy. The proposed framework can be applied in designing signed, unsigned, directed, or undirected networks. It should be noted that this work is the first to apply memetic algorithms in the design of controllable networks. We chose memetic algorithms because they have been shown to be more efficient and more effective than the standard genetic algorithms in solving some optimization problems. Our simulation results provide an additional demonstration of their efficiency and effectiveness.

Networks, representing attitudinal survey data, expose the structure of opinion-based groups. We make use of these network projections to identify the groups reliably through community detection algorithms and to examine social-identity-based groups. Our goal is to present a method for revealing polarization and opinion-based groups in attitudinal surveys. This method can be broken down into the following steps: data preparation, construction of similarity-based networks, algorithmic identification of opinion-based groups, and identification of important items for community structure. We assess the method’s performance and possible scope for applying it to empirical data and to a broad range of synthetic data sets. The empirical data application points out possible conclusions (i.e. social-identity polarization), whereas the synthetic data sets mark out the method’s boundaries. Next to an application example on political attitude survey, our results suggest that the method works for various surveys but is also moderated by the efficacy of the community detection algorithms. Concerning the identification of opinion-based groups, we provide a solid method to rank the item’s influence on group formation and as a group identifier. We discuss how this network approach for identifying polarization can classify non-overlapping opinion-based groups even in the absence of extreme opinions.

Any collection can be ranked. Sports and games are common examples of ranked systems: players and teams are constantly ranked using different methods. The statistical properties of rankings have been studied for almost a century in a variety of fields. More recently, data availability has allowed us to study rank dynamics: how elements of a ranking change in time. Here, we study the rank distributions and rank dynamics of 12 datasets from different sports and games. To study rank dynamics, we consider measures that we have defined previously: rank diversity, change probability, rank entropy, and rank complexity. We also introduce a new measure that we call “system closure” that reflects how many elements enter or leave the rankings in time. We use a random walk model to reproduce the observed rank dynamics, showing that a simple mechanism can generate similar statistical properties as the ones observed in the datasets. Our results show that while rank distributions vary considerably for different rankings, rank dynamics have similar behaviors, independently of the nature and competitiveness of the sport or game and its ranking method. Our results also suggest that our measures of rank dynamics are general and applicable for complex systems of different natures.