Algebraic connectivity of graphs
λ₂ (2nd-smallest Laplacian eigenvalue) = algebraic connectivity; >0 iff connected; Fiedler vector bipartitions
Graph Algorithms
12 curated papers.
Discriminative Community Detection for Multiplex Networks
Per-layer normalized Laplacian → spectral community detection; discriminative objective separates two network configurations (e.g. crisis vs baseline)
Fast unfolding of communities in large networks
Louvain: greedy modularity maximization by local node moves + community collapse, near-linear in edges
Finding and evaluating community structure in networks
Modularity Q — fraction of within-community edges minus the random-wiring expectation
Functional cartography of complex metabolic networks
Participation coefficient + within-module-degree z-score → universal node roles (specialist vs connector)
Mathematical Formulation of Multilayer Networks
Rank-4 adjacency tensor → supra-adjacency / supra-Laplacian; multiplex participation coefficient, multilayer eigenvector centrality, multiplex PageRank, Von Neumann entropy, diffusion τ=1/λ₂
Multilayer Networks
Definitive multilayer/multiplex taxonomy (node-layer tuples, aspects); reconciles the competing formalisms
Finding multifaceted communities in multiplex networks
Novel multiplex modularity measure for communities that differ per layer
Navier-Stokes Framework for Systemic Risk
Contagion decay κ = √(λ₂/D) — reuses algebraic connectivity as a flow-based systemic-risk metric
State of the Art in Multilayer Network Visualization
Survey of multilayer layout families (stacked planes, node-link, concentric-ring) and their tradeoffs
Structural measures for multiplex networks
Multiplex structural measures: multiplex participation coefficient, edge overlap/reinforcement, multiplex clustering
The Topology of Interbank Payment Flows
Fedwire is scale-free core-periphery; eigenvector centrality identifies money-center hubs whose failure cascades beyond direct exposure