Contents

1 Structural descriptors
 1.1 Basic node, edge, and layer properties
  1.1.1 Node and layer activity
  1.1.2 Layer aggregation
  1.1.3 Node degree, participation coefficient, cartography
  1.1.4 Edge overlap, reinforcement
 1.2 Inter-layer degree correlations
  1.2.1 Node ranking
  1.2.2 Interlayer degree correlation coefficients
  1.2.3 Interlayer degree correlation functions
2 Models of multi-layer networks
 2.1 Null models
  2.1.1 Null-models of node and layer activity
 2.2 Growing multiplex networks
  2.2.1 Linear preferential attachment
  2.2.2 Non-linear preferential attachment
  2.2.3 Utilities
 2.3 Multiplex networks with inter-layer degree correlations
  2.3.1 Models based on simulated annealing
3 Dynamics on multi-layer networks
 3.1 Interacting opinions - Multilayer ising model
 3.2 Biased random walks
  3.2.1 Stationary distribution
  3.2.2 Entropy rate