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Complex graph
Mathematical structure composed of nodes and edges exhibiting non-trivial organizational properties, emerging from interactions between many interconnected elements.
Topological analysis
Study of invariant structural properties of a network, independent of its geometric representation, allowing characterization of its fundamental organization.
Small-world network
Network structure combining a high clustering coefficient with a low characteristic average distance, promoting rapid information propagation while maintaining strong local cohesion.
Scale-free network
Type of network whose degree distribution follows a power law, characterized by the presence of few highly connected nodes (hubs) and many poorly connected nodes.
Barabási-Albert model
Network generation model based on preferential attachment, explaining the natural emergence of scale-free structures through continuous growth and preferential connection to existing nodes.
Dynamics on networks
Study of temporal processes (propagation, synchronization, opinion) evolving on the fixed structure of a network, where topology strongly influences the global behavior of the system.
Percolation theory
Theoretical framework analyzing emergent connectivity in random networks, determining critical thresholds for giant component formation and structural phase transition.
Network synchronization
Emerging phenomenon where interconnected dynamic units adjust their temporal behaviors to achieve a coherent state, crucial in neural and communication networks.
Information diffusion
Process of propagation of signals or influences through a network, modeled by differential equations or stochastic processes depending on the topological structure.
Resilience analysis
Evaluation of a network's ability to maintain its functionality in the face of failures or attacks, quantifying structural robustness and fault tolerance.
Assortativity metric
Coefficient measuring the correlation between the degrees of connected nodes, determining whether similar nodes tend to connect to each other (assortative) or to different nodes (disassortative).
Configuration model
Generator of random networks with specified degree distribution, allowing the creation of networks with controlled structural properties for comparative study.
Stochastic graph theory
Mathematical formalization of networks with random components, integrating probabilities to model uncertainty in connections and evolutionary dynamics.