To meet the demands of future wireless networks, antenna arrays must scale from massive multiple-input multiple-output (MIMO) to gigantic MIMO, involving even larger numbers of antennas. To address the hardware and computational cost of gigantic MIMO, several strategies are available that shift processing from the digital to the analog domain. Among them, microwave linear analog computers (MiLACs) offer a compelling solution by enabling fully analog beamforming through reconfigurable microwave networks. Prior work has focused on fully-connected MiLACs, whose ports are all interconnected to each other via tunable impedance components. Although such MiLACs are capacity-achieving, their circuit complexity, given by the number of required impedance components, scales quadratically with the number of antennas, limiting their practicality. To solve this issue, in this paper, we propose a graph theoretical model of MiLAC facilitating the systematic design of lower-complexity MiLAC architectures. Leveraging this model, we propose stem-connected MiLACs as a family of MiLAC architectures maintaining capacity-achieving performance while drastically reducing the circuit complexity. Besides, we optimize stem-connected MiLACs with a closed-form capacity-achieving solution. Our theoretical analysis, confirmed by numerical simulations, shows that stem-connected MiLACs are capacity-achieving, but with circuit complexity that scales linearly with the number of antennas, enabling high-performance, scalable, gigantic MIMO.

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