We introduced a novel interconnect topology named Equality with high-performance and low diameter. Equality is designed based on chordal ring networks. It advances previous discussed chordal ring topologies by a set of systematic linking strategies and routing rules. The Equality topology can be used construct low diameter networks with reasonably low router radices. Equality interconnects are highly symmetric and hence cabling rule and routing logic are simple. Compared with other networks, the Equality topology is flexible in total number of routers, where any even number is allowed. Equality can be applied in many applications including supercomputing, data center, cloud service, and enterprise cluster solutions. We evaluated Equality's performance using open-source BookSim 2.0 package. The benchmarks of 10 traffic models for the system constructed using 40-port switches are presented to assess the network performance, compared with the popular 3-tier fat-tree (3-T FT) structure. This case mimics the network architecture and the parameters of the switches of the top #1 supercomputer, Summit. These results show that Equality networks perform better than 3-T FTs with lower latency under five large-packet-size simulations (LPSS) by 3 traffic models: uniform, neighbor and transpose. The latency is better than 3-T FT in four of five LPSSs by bitrev and randperm and also in three of five LPSSs by bitrot and shuffle. The third group of the results has lower latency compared with that of fat-tree in three hot-spot and three non-uniform traffic conditions in all five LPSSs larger than 16 flits. The zero-load latency of Equality networks are lower than that of 3-T FT under the same simulation constraints.