The distribution of path lengths of self avoiding walks on Erdős–Rényi networks

  title={The distribution of path lengths of self avoiding walks on Erdős–R{\'e}nyi networks},
  author={Ido Tishby and Ofer Biham and Eytan Katzav},
  journal={Journal of Physics A: Mathematical and Theoretical},
We present an analytical and numerical study of the paths of self avoiding walks (SAWs) on random networks. Since these walks do not retrace their paths, they effectively delete the nodes they visit, together with their links, thus pruning the network. The walkers hop between neighboring nodes, until they reach a dead-end node from which they cannot proceed. Focusing on Erdős–Rényi networks we show that the pruned networks maintain a Poisson degree distribution, p t ( k ) , with an average… 

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