1. A hierarchical network comprising: a plurality of lower layer networks, each of said lower layer networks being a p-array, n-cube network where p and n are integers greater than 1, and connecting a plurality of nodes provided for each lower layer network, wherein part of said plurality of nodes are selected as a plurality of gate nodes in said each lower layer network; and an upper layer network being a p-array, n-cube networks where p and n are integers greater than 1, and connecting a group of gate nodes selected for said plurality of lower layer networks; wherein said plurality of lower layer networks, said upper layer network and said group of gate nodes establish communication between nodes belonging to different lower layer networks, in such a manner that communication provided by a first node included in a plurality of nodes connected by a first one of said plurality of lower layer networks is first relayed by way of said first lower layer network to a first gate node included in a plurality of gate nodes selected for said first lower layer network, said first gate node being nearest to said first node among said plurality of gate nodes selected for said first lower layer network; said communication is further relayed by said upper layer network to a second gate node included in a plurality of gate nodes selected for a second one of said plurality of lower level networks which connect a plurality of nodes which includes a second node to which said communication is to be transferred, said second gate node being one nearest to said second node among said plurality of gate nodes selected for said second lower layer network; and said communication is further transferred by way of said second lower layer network from said second gate node to said second node.