Tensor networks (TNs) provide structured low-rank representations for high-dimensional data and have become important tools in scientific computing and machine learning. This thesis investigates adaptive tensor network topology learning, focusing on topology as an explicit inductive bias that governs both expressivity and computational cost. While classical formats such as Tensor-Train, Tensor-Ring, and Hierarchical Tucker are efficient, their fixed structures restrict flexibility. To address this limitation, the present work develops a framework for feasibility-aware topology adaptation under explicit computational constraints. A local topology search strategy is proposed for arbitrary-graph tensor networks. Network structure is encoded as a binary edge representation and explored through neighborhood-based modifications.