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The problem of measuring the structural complexity of logic networks is examined. A complexity measure π(N) is proposed which is the total number of input-output paths in an acyclic network N. π(N) is easily computed by representing network structure in matrix form. It is shown that simple upper bounds on the number of tests required by a combinational network N can be derived from π(N). These bounds are fairly tight when N contains little or no fan-out. The path complexity of combinational functions is defined and briefly discussed.