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5. DYNAMICS IN THE NETWORKS

5. DYNAMICS IN THE NETWORKS. Something going on. Network dynamics: global goal local goal Flow in complex networks: ideas innovations computer viruses problems. Network dynamics.

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5. DYNAMICS IN THE NETWORKS

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  1. 5. DYNAMICS IN THE NETWORKS Something going on

  2. Network dynamics: • global goal • local goal • Flow in complex networks: • ideas • innovations • computer viruses • problems

  3. Network dynamics • The time scale governing the dynamics of the network is comparable to that characterizing the network connectivity • Evolutionary models with optimization mechanisms: • Parameterization • Simulated annealing

  4. Global vs local optimization • Design: the goal is to optimize global quantity (distance, clustering, density, ...) • Evolution: decision taken at node level

  5. Evolution • Bornholdt & Rohlf: Global criticality from local dynamics • Network of interconnected binary elements • The dynamics reaches an attractor • Change the connectivity of a node according to its behavior during the attractor • Evolution towards critical value of connectivity • Phase transition at the critical value: frozen state- dynamical state

  6. Optimization • Global goal: • Distance: related to minimal cost in transportation • Number of connections: costly connections • A combination of parameters • Initial configuration: random graph • Change connections • Accept if there is an improvement • Stars vs trees

  7. Flow in complex networks • Viruses • Information

  8. Virus spreading • SIS (susceptible-infected-susceptible) model • Each healthy (susceptible) individual is infected with rate  when it has at least one infected neighbor • Infected nodes are cured (become susceptible) with rate  (=1 without lost of generality)

  9. Known results • Regular lattices • Random graphs •  Non zero epidemic threshold • >= c: spreads and become persistent • < c: the infection dies out exponentially • Equivalent to a nonequilibrium phase transition

  10. Scale free networks • Absence of an epidemic threshold • Due to the unboundedness of the connectivity fluctuations (<k2>with a power law distribution) • The same fact that make scale-free networks to be robust against random failures makes it very sensitive to the spread of infections

  11. Virus prevalence • Density of infected nodes in surviving infections

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