Statistical Mechanics of Complex Networks

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ComplNetwPicture


Complex networks-a way to describe a large class of complex systems: Introduction to the complex networks recently under study with network techniques and introduction to the terminology used in their characterization.

Main topics:

  • Random networks
    • G(n,p) G(n,M) ensembles
    • Subgraphs characterization
    • Hamiltonian cycles
    • Coloring problem
  • Random Graphs
    • Emergence of the giant component
    • Indipendet sets
    • Vertex Cover problem
  • Phenomenology of scale-free networks
    • Growing scale-free networks models
    • Preferential attachment
    • Superlinear preferential attachment
    • Fitness model
  • Random scale-free networks
    • Generation of random scale-free networks
    • Diameter
    • Robustness under failure fragility under attack
  • Subgraphs composition of complex networks
    • Loops
    • Cliques
    • K-cores
  • Dynamics on networks
    • Ising model on small-worl networks and scale-free networks
    • Epidemic spreading
  • Weigthed networks
    • Models
    • Synchonization on weighted networks
  • Community detection
    • Givan-Newman method
    • Spectral method
  • Time dependence of dynamical systems on networks
    • Time dependence of epidemic spreading
    • Community detection methods using synchronization

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