Markov clustering (MCL) is an effective unsupervised pattern recognition algorithm for data clustering in high-dimensional feature space that simulates stochastic flows on a network of sample similarities to detect the structural organization of clusters in the data. However, it presents two main drawbacks: (1) its community detection performance in complex networks has been demonstrating results far from the state-of-the-art methods such as Infomap and Louvain, and (2) it has never been generalized to deal with data nonlinearity. In this work both aspects, although closely related, are taken as separated issues and addressed as such. Regarding the community detection, field under the network science ceiling, the crucial issue is to convert the unweighted network topology into a ‘smart enough’ pre-weighted connectivity that adequately steers the stochastic flow procedure behind Markov clustering. Here a conceptual innovation is introduced and discussed focusing on how to leverage network latent geometry notions in order to design similarity measures for pre-weighting the adjacency matrix used in Markov clustering community detection. The results demonstrate that the proposed strategy improves Markov clustering significantly, to the extent that it is often close to the performance of current state-of-the-art methods for community detection. These findings emerge considering both synthetic ‘realistic’ networks (with known ground-truth communities) and real networks (with community metadata), even when the real network connectivity is corrupted by noise artificially induced by missing or spurious links. Regarding the nonlinearity aspect, the development of algorithms for unsupervised pattern recognition by nonlinear clustering is a notable problem in data science. Minimum Curvilinearity (MC) is a principle that approximates nonlinear sample distances in the high-dimensional feature space by curvilinear distances, which are computed as transversal paths over their minimum spanning tree, and then stored in a kernel. Here, a nonlinear MCL algorithm termed MC-MCL is proposed, which is the first nonlinear kernel extension of MCL and exploits Minimum Curvilinearity to enhance the performance of MCL in real and synthetic high-dimensional data with underlying nonlinear patterns. Furthermore, improvements in the design of the so-called MC-kernel by applying base modifications to better approximate the data hidden geometry have been evaluated with positive outcomes. Thus, different nonlinear MCL versions are compared with baseline and state-of-art clustering methods, including DBSCAN, K-means, affinity propagation, density peaks, and deep-clustering. As result, the design of a suitable nonlinear kernel provides a valuable framework to estimate nonlinear distances when its kernel is applied in combination with MCL. Indeed, nonlinear-MCL variants overcome classical MCL and even state-of-art clustering algorithms in different nonlinear datasets. This dissertation discusses the enhancements and the generalized understanding of how network geometry plays a fundamental role in designing algorithms based on network navigability.

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