Freight rail networks serve a key role in transporting bulk goods to accommodate changing market demands and to serve public needs. Network analyses of such systems can provide important insights into enhancing transportation efficiency and system resilience. This paper develops and investigates a topological analysis model for network efficiency, which is associated with the connectedness of a network's nodes by its links and their corresponding network attributes. This model allows analyzing network topologies with or without assigned weights to their nodes and links based on different attributes. Key attributes may include physical length of links, commodity types and volume of goods transported through links, and dwell-time at nodes, and origination termination volumes of goods, types of goods moved, and origins and destination of goods. The model presented here enables (1) defining distinctions that may be employed for the assignment of node and link weights, (2) gaining an understanding of node and link criticality, and (3) providing methods for objectively maintaining and enhancing network performance. Such analyses can inform rail managers and executives in planning expansions, route or freight changes, or preparations for potential node or link failures. A case study of an aggregate U.S. freight rail network along with other example topologies is presented to demonstrate the use of selected network attributes and their influence on connectedness efficiency and the impacts of node and link failures on the overall transport efficiency.