A Novel Algorithm for Detecting Protein Complexes with the Breadth First Search
Figure 1
Example to illustrate the clustering process. This example network has 12 vertices, and every edge has confidence. Suppose the weighted density threshold . The vertex 0 is taken as a seed protein and the original cluster 0 is constructed. In the first step of the breadth first search, the vertex 1 has the highest edge weight 0.75 among the neighbors of the vertex 0. We add vertex 1 to the cluster and this cluster now has the weighted density 0.75 that is bigger than the density threshold 0.2. Similarly, the vertices 2, 3, 4, and 5 are added to the cluster in sequence and the cluster now has the weighted density 0.23 which is still more than the threshold 0.2. Next, the neighbors of vertex 4 are considered. Of these, vertex 6 has the highest edge weight 0.52 and is added to the cluster. However, the weighted density of the cluster is 0.19 and less than the threshold 0.2. Thus, the vertex 6 is removed and the neighbor of the vertex 3 is examined. Because the weighted value between the vertex 3 and its neighboring vertex 9 is 0.51 and less than 0.52, the vertex 9 is not added to the cluster. When the neighbors of the vertex 2 are checked, the vertex 10 is added to the cluster. Since the weighted density of the cluster is less than 0.2, the vertex 10 is removed. And, likewise, the vertex 11 is not added to the cluster. We stop extending the cluster and output the final cluster . For simplicity, the elimination of redundant clusters is not shown in this figure.
