Alzheimer's disease (AD) and Lewy body dementia (LBD) present overlapping clinical features yet require distinct diagnostic strategies. While neuroimaging-based brain network analysis is promising, atlas-based representations may obscure individualized anatomy. Gyral folding-based networks using three-hinge gyri provide a biologically grounded alternative, but inter-individual variability in cortical folding results in inconsistent landmark correspondence and highly irregular network sizes, violating the fixed-topology and node-alignment assumptions of most existing graph learning methods, particularly in clinical datasets where pathological changes further amplify anatomical heterogeneity. We therefore propose a probability-invariant random-walk-based framework that classifies individualized gyral folding networks without explicit node alignment. Cortical similarity networks are built from local morphometric features and represented by distributions of anonymized random walks, with an anatomy-aware encoding that preserves permutation invariance. Experiments on a large clinical cohort of AD and LBD subjects show consistent improvements over existing gyral folding and atlas-based models, demonstrating robustness and potential for dementia diagnosis.