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Distribution of shortest path lengths on trees of a given size in subcritical Erdős-Rényi networks
Barak Budnick1, Ofer Biham1, Eytan Katzav1
1Racah Institute of Physics, The Hebrew University, Jerusalem 9190401, Israel.
Abstract:
In the subcritical regime Erdős-Rényi (ER) networks consist of finite tree components, which are nonextensive in the network size. The distribution of shortest path lengths (DSPL) of subcritical ER networks was recently calculated using a topological expansion [E. Katzav, O. Biham, and A. K. Hartmann, Phys. Rev. E 98, 012301 (2018)2470-004510.1103/PhysRevE.98.012301]. The DSPL, which accounts for the distance ℓ between any pair of nodes that reside on the same finite tree component, was found to follow a geometric distribution of the form P(L=ℓ|L<∞)=(1-c)c^{ℓ-1}, where 0
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