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Percolation on a maximally disassortative network

We propose a maximally disassortative (MD) network model which realizes a maximally negative degree-degree correlation, and study its percolation transition to discuss the effect of a strong degree-degree correlation on the percolation critical behaviors. Using the generating function method for bipartite networks, we analytically derive the percolation threshold and the order parameter critical exponent, $β$. For the MD scale-free networks, whose degree distribution is $P(k) \sim k^{-γ}$, we show that the exponent, $β$, for the MD networks and corresponding uncorrelated networks are same for $γ>3$ but are different for $2<γ<3$. A strong degree-degree correlation significantly affects the percolation critical behavior in heavy-tailed scale-free networks. Our analytical results for the critical exponents are numerically confirmed by a finite-size scaling argument.