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Network segregationâ€"a critical problem in real-life networksâ€"can reveal the emergence of conflicts or signal an impending collapse of the whole system. However, the strong heterogeneity of such networks and the various definitions for key nodes continue to pose challenges that limit our ability to foresee segregation and to determine the main drivers behind it. In this paper, we show that a multi-agent leaderâ€"follower consensus system can be utilized to define a new index, named leadership, to identify key leaders in real-life networks. And then, this paper explores the emergence of network segregation that is driven by these leaders based on the removal or the rewiring of the relations between different nodes in agreement with their contribution distance. We finally show that the observed leaders-driven segregation dynamics reveals the dynamics of heterogeneous attributes that critically influence network structure and its segregation. Thus, this paper provides a theoretical method to study complex social interactions and their roles in network segregation, which ultimately leads to a closed-form explanation for the emergence of imbalanced network structure from an evolutionary perspective. [ABSTRACT FROM AUTHOR]

Swarmalators are entities with the simultaneous presence of swarming and synchronization that reveal emergent collective behavior due to the fascinating bidirectional interplay between phase and spatial dynamics. Although different coupling topologies have already been considered, here we introduce time-varying competitive phase interaction among swarmalators where the underlying connectivity for attractive and repulsive coupling varies depending on the vision (sensing) radius. Apart from investigating some fundamental properties like conservation of center of position and collision avoidance, we also scrutinize the cases of extreme limits of vision radius. The concurrence of attractiveâ€"repulsive competitive phase coupling allows the exploration of diverse asymptotic states, like static Ď€, and mixed phase wave states, and we explore the feasible routes of those states through a detailed numerical analysis. In sole presence of attractive local coupling, we reveal the occurrence of static cluster synchronization where the number of clusters depends crucially on the initial distribution of positions and phases of each swarmalator. In addition, we analytically calculate the sufficient condition for the emergence of the static synchronization state. We further report the appearance of the static ring phase wave state and evaluate its radius theoretically. Finally, we validate our findings using Stuartâ€"Landau oscillators to describe the phase dynamics of swarmalators subject to attractive local coupling. [ABSTRACT FROM AUTHOR]