In recent years, real-time data mining for large-scale timeevolving graphs is becoming a hot research topic. Most of the prior arts target relatively static graphs and also process them in store-and-process batch processing model. In this paper we propose a method of applying on-the-fly and incremental graph stream computing model to such dynamic graph analysis. To process large-scale graph streams on a cluster of nodes dynamically in a scalable fashion, we propose an incremental large-scale graph processing model called "Incremental GIM-V (Generalized Iterative Matrix-Vector Multiplication)". We also design and implement UNICORN, a system that adopts the proposed incremental processing model on top of IBM InfoSphere Streams. Our performance evaluation demonstrates that our method achieves up to 48% speedup on PageRank with Scale 16 Log-normal Graph (vertexes=65,536, edges=8,364,525) with 4 nodes, 3023% speedup on Random walk with Restart with Kronecker Graph with Scale 18 (vertexes=262,144, edges=8,388,608) with 4 nodes against original GIM-V.