Table 4 Definitions of topological features in graph theory
Topological feature | Definition | |
|---|---|---|
1 | Center | Node with eccentricity equal to the radius |
2 | Density | Defined as \(d=\frac{2N_E}{N_v(N_v-1)}\) for an undirected graph, where \(N_E\) and \(N_v\) are the number of edges and nodes in a graph G |
3 | Radius | Minimum eccentricity of a graph |
4 | Diameter | Maximum eccentricity of a graph |
5 | Periphery | Periphery is a subgraph with eccentricity equal to the diameter of G |
6 | Triangle | Number of triangles having a node v as one vertex |
7 | Transitivity | Fraction of all possible triangles present in G |
8 | Degrees | Nnumber of edges connected to the node |
9 | In degree | Number of head ends adjacent to a node |
10 | Out degree | Number of tail ends adjacent to a node |
11 | Weighted degree (Newman, 2001) | Summation of edges connected to the node |
12 | Eccentricity (Harary & Norman, 1953) | Maximum distance from node v to all other nodes in G |
13 | Hub (Kleinberg et al., 2011) | Number of highly authoritative nodes a node v is pointing to |
14 | Authority (Kleinberg et al., 2011) | Amount of valuable information that a node v carries |
15 | PageRank (Page et al., (1999) | Importance of a node v in the graph G |
16 | Closeness centrality (Sabidussi, 1966) | Time it takes to move from node v to other nodes in the graph G |
17 | Betweenness centrality (Brandes, 2001) | Sum of the fraction of all-pairs shortest paths that pass through a node v |
18 | Information centrality (Brandes & Fleischer, 2005) | Current-flow closeness centrality based on effective resistance between nodes in a network |
19 | Harmonic centrality (Marchiori & Latora, 2000) | Sum of the reciprocal of the shortest path distances from node v to all other nodes in G |
20 | Eigenvector centrality (Bonacich, 1987) | Connectivity or transitive influence of a node v |