Models and Methods for Random Networks

Percolation 2: Site and Continuum Percolation Models

We finish the study of bond percolation on the 2-dim lattice. We then move to percolation in more general graphs than the lattice and the tree. Few quantitative results can be rigorously assessed, but the phase transition observed for tree and lattice bond models extends to site and continuum percolation as well.

Course Materials

Homework

Deadline

  • Homework 2 due today.

Illustrations

  • This animation shows the evolution of the random geometric graph G_{geom} as the relative node density \lambda r^2 is gradually increased. Essentially, nodes are raining down randomly on the 2D plane, and two nodes are connected if they are close enough. The percolation threshold of approx. 1.43 can be observed.

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