Context: Several metrics have been proposed to measure the extent to which class members are related. Connectivity-based class cohesion metrics measure the degree of connectivity among the class members. Objective: We propose a new class cohesion metric that has higher discriminative power than any of the existing cohesion metrics. In addition, we empirically compare the connectivity and non-connectivity-based cohesion metrics. Method: The proposed class cohesion metric is based on counting the number of possible paths in a graph that represents the connectivity pattern of the class members. We theoretically and empirically validate this path connectivity class cohesion (PCCC) metric. The empirical validation compares seven connectivity-based metrics, including PCCC, and 11 non-connectivity-based metrics in terms of discriminative and fault detection powers. The discriminative-power study explores the probability that a cohesion metric will incorrectly determine classes to be cohesively equal when they have different connectivity patterns. The fault detection study investigates whether connectivity-based metrics, including PCCC, better explain the presence of faults from a statistical standpoint in comparison to other non-connectivity-based cohesion metrics, considered individually or in combination. Results: The theoretical validation demonstrates that PCCC satisfies the key cohesion properties. The results of the empirical studies indicate that, in contrast to other connectivity-based cohesion metrics, PCCC is much better than any comparable cohesion metric in terms of its discriminative power. In addition, the results also indicate that PCCC measures cohesion aspects that are not captured by other metrics, wherein it is considerably better than other connectivity-based metrics but slightly worse than some other non-connectivity-based cohesion metrics in terms of its ability to predict faulty classes. Conclusion: PCCC is more useful in practice for the applications in which practitioners need to distinguish between the quality of different classes or the quality of different implementations of the same class.