The connective constant of a quasi-transitive infinite graph is a measure for the asymptotic growth rate of the number of self-avoiding walks of length n from a given starting vertex. On edge-labelled graphs the formal language of self-avoiding walks is generated by a formal grammar, which can be used to calculate the connective constant of the graph. Christian Lindorfer discusses the methods in some examples, including the infinite ladder-graph and the sandwich of two regular infinite trees. Contents Graph Height Functions and Bridges Self-Avoiding Walks on One-Dimensional Lattices The Algebraic Theory of Context-Free Languages The Language of Walks on Edge-Labelled Graphs Target Groups Researchers and students in the fields of graph theory, formal language theory and combinatorics Experts in these areas The Author Christian Lindorfer wrote his master's thesis under the supervision of Prof. Dr. Wolfgang Woess at the Institute of Discrete Mathematics at Graz University of Technology, Austria.