Collective behavior in networks

Collective behavior in networks is coordinated or correlated activity that emerges from interactions among agents connected by a network. It can arise without central control, through local rules and the network’s structure.

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Network contagion: The spread of behaviors, information, or states through interactions among connected individuals. It shows how local transmission can produce widespread collective change.
Graph theory: The mathematical study of structures made of vertices and edges. It supplies the formal language for describing who is connected to whom.
Flocking: Coordinated movement by groups of animals arising from interactions among nearby individuals. Flocking is a clear case of collective motion emerging from local rules.
Centralized control: An organizational arrangement in which a central authority directs decisions or actions. Networked collective behavior can coordinate activity without commands from a central authority.
Synchronization: The adjustment of interacting systems toward coordinated timing or shared rhythms. Coupled agents can align their activity even without a central coordinator.
Complex network: A network whose structure has properties not captured by simple regular or random graphs. Real interaction systems often have uneven degrees, clustering, or community structure.
Opinion dynamics: Models of how opinions change through interactions among individuals. They connect network structure to consensus, polarization, and persistent disagreement.
Mean-field theory: An approximation that replaces interactions with a population-wide average effect. It suppresses specific network connections that can determine collective outcomes.
Emergence: The appearance of system-level properties that are not evident from isolated components alone. Collective patterns are system-level outcomes of interactions among networked agents.
Agent-based model: A computational model that represents individual agents and their rules of interaction. It can reveal how specified local behaviors generate population-level patterns.