Estimating a representative and discriminative brain network atlas (BNA) is a nascent research field in mapping a population of brain networks in health and disease. Although limited, existing BNA estimation methods have several limitations. First, they primarily rely on a similarity network diffusion and fusion technique, which only considers node degree as a topological measure in the cross-network diffusion process, thereby overlooking rich topological measures of the brain network (e.g., centrality). Second, both diffusion and fusion techniques are implemented in fully unsupervised manner, which might decrease the discriminative power of the estimated BNAs. To fill these gaps, we propose a supervised multi-topology network cross-diffusion (SM-netFusion) framework for estimating a BNA satisfying : (i) well-representativeness (captures shared traits across subjects), (ii) well-centeredness (optimally close to all subjects), and (iii) high discriminativeness (can easily and efficiently identify discriminative brain connections that distinguish between two populations). For a specific class, given the cluster labels of the training data, we learn a weighted combination of the topological diffusion kernels derived from degree, closeness and eigenvector centrality measures in a supervised manner. Specifically, we learn the cross-diffusion process by normalizing the training brain networks using the learned diffusion kernels. Our SM-netFusion produces the most centered and representative template in comparison with its variants and state-of-the-art methods and further boosted the classification of autistic subjects by 5-15%. SM-netFusion presents the first work for supervised network cross-diffusion based on graph topological measures, which can be further leveraged to design an efficient graph feature selection method for training predictive learners in network neuroscience.