This chapter introduces foundational concepts from graph theory and matrix algebra that underpin network analysis. It begins by defining networks, nodes, links, and the key notion of strong connectivity. Matrix algebra tools are then presented, including basic operations and permutation matrices to formalize reducibility and irreducibility. A bridge between graph structures and matrix representations is built through adjacency and incidence matrices. The equivalence between physical and algebraic properties is then established: strong connectivity corresponds to matrix irreducibility, while flow conservation aligns with the premagic property. These relationships set the stage for the Perron-Frobenius theorem, which guarantees a unique, stable equilibrium flow in any strongly connected network. Lastly, the chapter introduces computational tools, such as the generalized inverse, that support the implementation of these ideas in the Ideal Flow Network (IFN) model. The material is presented sequentially to reinforce understanding from first principles and support practical application in network design and analysis.