Network research has been focused on studying the properties of a single isolated network,
which rarely exists. We develop a general analytical framework for studying percolation of n
interdependent networks. We illustrate our analytical solutions for three examples:(i) For any
tree of n fully dependent Erdős-Rényi (ER) networks, each of average degree k¯, we find
that the giant component is P∞= p [1-exp⁡(-k¯ P∞)] n where 1-p is the initial fraction of
removed nodes. This general result coincides for n= 1 with the known second-order phase …

Network research has been focused on studying the properties of a single isolated network,
which rarely exists. We develop a general analytical framework for studying percolation of n
interdependent networks. We illustrate our analytical solutions for three examples:(i) For any
tree of n fully dependent Erdos-R'enyi (ER) networks, each of average degree k, we find that
the giant component P∞= p [1-(-kP∞)]^ n where 1-p is the initial fraction of removed nodes.
This general result coincides for n= 1 with the known second-order phase transition for a …