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Most networks of interest do not live in isolation. Instead they form components of larger systems in which multiple networks with distinct topologies coexist and where elements distributed amongst different networks may interact directly. The authors derive exact expressions for the percolation threshold describing the onset of large-scale connectivity in the system of networks and each network individually. They show that the percolation threshold in an individual network can be significantly lowered once "Hidden" connections to other networks are considered. They show applications of the framework to two real-world systems involving communications networks and socio-technical congruence in software systems.
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