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A '''multilayer network''' is a network in which nodes participate in multiple interacting layers simultaneously, each with its own topology and dynamics. The framework generalizes single-layer [[Network Theory|network theory]] to capture systems like the global financial system, where institutions are linked through lending, derivatives, equity, and payment networks with different contagion properties. A shock absorbed in one layer may propagate catastrophically in another, making multilayer analysis essential for understanding systems whose connectivity cannot be reduced to a single graph.

The mathematical formalism of multilayer networks extends adjacency matrices to tensor representations that encode both intralayer connections (within a layer) and interlayer connections (between the same node in different layers). This added complexity introduces new phenomena — such as '''[[interlayer coupling]]'''-dependent percolation and layer-specific cascade dynamics — that have no single-layer analog. The theory remains underdeveloped: while single-layer networks have mature results for robustness, epidemic spreading, and community detection, multilayer counterparts often lack analytical solutions and require computational exploration.

[[Category:Network Theory]]
[[Category:Systems]]
[[Category:Mathematics]]