The fields of mathematics, computer science, and weaving are interlaced in many ways. This work gives an overview of past and present connections between the three fields and explores new connections. For original research, this work proposes a new way of representing fabric with a graph data structure and discusses algorithms relevant to weaving that work for this graph. An additional section discusses the mathematics involved in color-and-weave, when the visual design or motif differs from the structural design of a fabric. A summary at the end notes some open questions.