This chapter provides a comprehensive framework for defining and analyzing Feynman integrals through a graph-theoretical perspective, with an emphasis on parametric representations such as Feynman, Schwinger, and Lee-Pomeransky parametrizations. We introduce Feynman parameters as integration variables, transforming from traditional loop momentum representations, and clarifying the combinatorial and algebraic structure of the integrals and underlying graphs. This approach not only simplifies loop number counting and the assignment of loop momentum but also establishes a systematic way for analyzing complex Feynman integrals encountered in quantum field theory. In the last section, we explore advanced topics, such as intersection numbers for Feynman integrals, which enable a unified framework for integral reduction.