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We show that fully connected two-hop wireless networks with K sources, Krelays and K destinations have K degrees of freedom both in the case oftime-varying channel coefficients and in the case of constant channelcoefficients (in which case the result holds for almost all values of constantchannel coefficients). Our main contribution is a new achievability schemewhich we call Aligned Network Diagonalization. This scheme allows the datastreams transmitted by the sources to undergo a diagonal linear transformationfrom the sources to the destinations, thus being received free of interferenceby their intended destination. In addition, we extend our scheme to multi-hopnetworks with fully connected hops, and multi-hop networks with MIMO nodes, forwhich the degrees of freedom are also fully characterized.

Degrees of Freedom of Two-Hop Wireless Networks: "Everyone Gets the Entire Cake"