Evolving graphs in the real world are large-scale and constantly changing, as hundreds of thousands of updates may come every second. Monotonic algorithms such as Reachability and Shortest Path are widely used in real-time analytics to gain both static and temporal insights and can be accelerated by incremental computing. Existing streaming systems adopt the incremental computing model and achieve either low latency or high throughput, but not both. However, both high throughput and low latency are required in real scenarios such as financial fraud detection. This paper presents RisGraph, a real-time streaming system that provides low-latency analysis for each update with high throughput. RisGraph addresses the challenge with localized data access and inter-update parallelism. We propose a data structure named Indexed Adjacency Lists and use sparse arrays and Hybrid Parallel Mode to enable localized data access. To achieve inter-update parallelism, we propose a domain-specific concurrency control mechanism based on the classification of safe and unsafe updates. Experiments show that RisGraph can ingest millions of updates per second for graphs with several hundred million vertices and billions of edges, and the P999 processing time latency is within 20 milliseconds. RisGraph achieves orders-of-magnitude improvement on throughput when analyses are executed for each update without batching and performs better than existing systems with batches of up to 20 million updates.