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Quantum walks are roughly analogous to classical random walks, and likeclassical walks they have been used to find new (quantum) algorithms. Whenstudying the behavior of large graphs or combinations of graphs it is useful tofind the response of a subgraph to signals of different frequencies. In sodoing we can replace an entire subgraph with a single vertex with frequencydependent scattering coefficients.  In this paper a simple technique for quickly finding the scatteringcoefficients of any quantum graph will be presented. These scatteringcoefficients can be expressed entirely in terms of the characteristicpolynomial of the graph's time step operator. Moreover, with these in hand wecan easily derive the "impulse response" which is the key to predicting theresponse of a graph to any signal. This gives us a powerful set of tools forrapidly understanding the behavior of graphs or for reducing a large graph intoits constituent subgraphs regardless of how they are connected.

A Simple Method for Finding the Scattering Coefficients of Quantum Graphs