Low-earth-orbit satellite constellations with hundreds to thousands of satellites are emerging as practical alternatives for providing various types of data services such as global networking and large-scale sensing. The network performance of these satellite constellations is strongly dependent on the topology of the inter-satellite links (ISLs) in such systems. This paper studies the effects of six different ISL topologies, coupled with three configurations of ground relay terminals, on path failure rate, path latency, and link transmission efficiency in an example highly-inclined Walker Delta constellation with 360 satellites. These network performance parameters are calculated in the presence of satellite failures in the constellation. Trade-offs between ISL connection density and overall performance are examined and quantified. Topologies with 4 active ISLs per satellite are shown to perform significantly better than topologies requiring fewer, especially as the average number of active ISLs per satellite becomes significantly less than three. Latencies for a topology requiring 3 active ISLs per satellite are shown to be between 15 and 60% higher than for a 4-ISL reference topology. Path availabilities for the 3-ISL topology are shown to be on the order of 30% lower for a benchmark case of 10 satellite failures. The performance of near-minimal topologies (e.g., an average of 2.2 active ISLs per satellite) is much worse. Latency reductions of 10-30% and path failure rate improvements on the order of 45% are shown to be obtainable by the inclusion of 2 to 5 strategically located ground relay stations