Large de bruijn graph based algorithm is widely used in genome assembly and metagenetic assembly. The scale of this kind of graphs - in some cases billions of vertices and edges - poses challenges to genome assembly problem. In this paper, a one-step bi-directed graph is used to abstract the problem of genome assembly. After that small world asynchronous parallel model (SWAP) is proposed to handle the edge merging operation predefined in the graph. SWAP aims at making use of the locality of computing and communication to explore parallelism for graph algorithm. Based on the above graph abstraction and SWAP model, an assembler is developed, and experiment results shows that a factor of 20 times speedup is achieved when the number of processors scales from 10 to 640 when testing on processing C.elegans data.