LAUSR

Centrosymmetry often mediates perfect state transfer (PST) in various complex systems ranging from quantum wires to photosynthetic networks. We introduce the deformed centrosymmetric ensemble (DCE) of random matrices H(λ)≡H_{+}+λH_{-}, where H_{+} is centrosymmetric while H_{-} is skew-centrosymmetric. The relative strength of the H_{±} prompts the system size scaling of the control parameter as λ=N^{-γ/2}. We propose two quantities, P and C, quantifying centro and skewcentrosymmetry, respectively, exhibiting second-order phase transitions at γ_{P}≡1 and γ_{C}≡-1. In addition, DCE posses an ergodic transition at γ_{E}≡0. Thus equipped with a precise control of the extent of centrosymmetry in DCE, we study the manifestation of γ on the transport properties of complex networks. We propose that such random networks can be constructed using the eigenvectors of H(λ) and establish that the maximum transfer fidelity F_{T} is equivalent to the degree of centrosymmetry P.