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If a genome has n COG-annotated genes and is clustered into m COG groups, then the vertex number of this GTN is m, and the sum of the degrees in this GTN is n-1.
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Centrality indices of a network include the Degree of each vertex (the number of physical connections a vertex has) and the Betweenness of a vertex which measure the number of shortest paths that the vertex lies on (high Betweenness signifies this vertex as one that resides on several short paths).
We run the BFS algorithm [8] on each vertex in the graph and determine the level of each vertex (the number of hops/edges from the root) in each of these BFS trees.
In particular, studies of protein-interaction networks have revealed complex relationships between vertex degree (number of neighbors in the network), network modularity (organization of the network into connected subnetworks), gene essentiality, gene pleiotropy, and so on.
The lower the edge-connectivity or vertex-connectivity number of a graph, therefore, the easier it is to disconnect, or break apart.
The degree centrality (DegC) of a vertex is the number of neighbors for the vertex in the graph and can be easily computed by counting the number of edges incident on the vertex.
The degree centrality of a vertex is the number of neighbors connected to the vertex and can be determined just based on the one-hop neighborhood knowledge.
On a BFS tree rooted at vertex r, the number of shortest paths for a vertex i at level l ((l quad>) 0) from the root r is the sum of the number of shortest paths from the root r to each the neighbors of vertex i (in the original graph) that are at level (l- 1 in the BFS tree.
Intelligibility is defined as the Pearson correlation between integration and the connectivity values of all vertices (the connectivity value of a vertex is the number of directly connected or adjacent vertices to that vertex) (Hillier et al. 1987).
Each Curvahedra piece corresponds to a vertex, and the number of branches in that piece corresponds to the number of edges coming from that vertex.
Each vertex in the network refers to a different sequence and the size of the vertex represents the number of identical sequences.
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