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Figure 1 | BMC Bioinformatics

Figure 1

From: Clustering under the line graph transformation: application to reaction network

Figure 1

(A) Example of clustering in an undirected network. Continuous and dash-dotted lines mean interaction between nodes. In addition, the dash-dotted line defines the only triangle where the node 1 (red) is one of the vertices. The node 1 has 4 neighbors (k i = 4), and among these neighbors only one pair is connected (n1 = 1). The total number of possible triangles that could go through node i is 6. Thus, the clustering coefficient has the value C1 = 1/6. High density of triangles means high clustering coefficient. (B) We show an example of the line graph transformation. The initial graph G corresponds to one subgraph which belongs to the Lysine Biosynthesis metabolic pathway. This graph is constructed by taking nodes as chemical compounds and edges as reactions. By applying the line graph transformation we find graph L(G), which is the reaction graph embedded in the graph G. The nodes of the graph L(G) are the reactions of the graph G [13].

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