Distribution of shortest path lengths on trees of a given size in subcritical Erdős-Rényi networks.

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.

Structure of networks that evolve under a combination of growth and contraction.

We present analytical results for the emerging structure of networks that evolve via a combination of growth (by node addition and random attachment) and contraction (by random node deletion). To this end we consider a network model in which at each time step a node addition and random attachment step takes place with probability P_{add} and a random node deletion step takes place with probability P_{del}=1-P_{add}. The balance between the growth and contraction processes is captured by the parameter η=P_{add}-P_{del}.