Closeness Centrality
| size |
| d(i,j) is the length of the shortest path between vertices i and j. The sum of CC
i
over all vertices gives the total Closeness Centrality of a given subgraph. |
[42]
|
Graph Diameter
| size |
| d(i,j) is the length of the shortest path between vertices i and j. GD is computed for all pairs (i,j), and reflects the longest path identified. |
[43]
|
Index of Aggregation
| size |
| A is the total number of vertices in the subgraph, and B is the total number of all given vertices in the graph. |
[15]
|
Assortative Mixing Coefficient
| distribution |
| k
1
and k
2
are the counts of edges of two vertices connected by a given edge. This measure reflects the edge-to-edge distribution over all edges of a graph. |
[44]
|
Entropy of the distribution of edges
| distribution |
| k is the count of edges of one vertex, and p(k) is the ratio of vertices that have k edges. |
[45]
|
Betweenness
| biological relevance |
| σ(j,i,k) is the total number of shortest connections between vertices j and k, where each shortest connection has to pass vertex i, and σ(j,k) is the total number of shortest connections between j and k. We computed σ(j,i,k) and σ(j,k) for the entire OPHID graph, but then only used vertices also present in the subgraph generated on the basis of a given gene-expression data set. |
[42]
|
Betweenness of all selected Vertices
| biological relevance | | As for Betweenness, but considering all selected vertices. |
[42]
|
Stress Centrality
| biological Relevance |
| σ(j,i,k) is the total number of shortest connections between vertices j and k, where each shortest connection has to pass vertex i. |
[42]
|
Connectivity
| density |
| A is the total number of edges realized in a given graph, and B is the maximum number of edges possible. |
[43]
|
Clustering Coefficient
| density |
| A is the total number of edges between the nearest neighbors of vertex i, and B is the maximum number of possible edges between the nearest neighbors of vertex i. The sum of CLUST
i
over all vertices gives the total Clustering Coefficient of a given subgraph. |
[46]
|
Number of edges divided by the number of vertices
| density |
| A is the total number of edges in a given graph, and B is the number of selected vertices in a given graph. |
-
|
Community
| density |
| A is the total number of edges, where both connected vertices are in the given subgraph, and B is the total number of edges, where one connected vertex is in the subgraph and the other vertex is outside it. |
[47]
|
Entropy
| density |
| where |E| is the total number of edges, |V| is the total number of vertices, and i(v) is the number of edges of vertex v. |
[48]
|
Graph Centrality
| density |
| max(d(i,j)) is the length of the shortest path between vertices i and j for a given vertex i. |
[42]
|
Number of walks of length n
| density |
| NW
i
is one walk with a length of n edges in the subgraph. |
[43]
|
Sum of the Wiener Number
| density |
| d(i,j) is the length of the shortest path between vertices i and j. We computed the Sum of the Wiener Number for each vertex. |
[43]
|
Total number of triangles of a subgraph and its dilation
| Modularity | | Given a subgraph g of graph G, the complement of g, denoted as g, is the subgraph implied by the set of vertices N(g) = N(G)\N(g) The dilation of g is the subgraph δ(g) implied by the vertices in g plus the vertices directly connected to a vertex in g. The coat of nearest neighbors of the subgraph is defined as DN(g) = δ(g)\N(g) The set of all valid triangles for g is defined as VT(g) = {x,y,z | (x,y,z ∈ N(δ(g)) ^ (x,y),(y,z),(z,x) ∈ E(δ(g))) ∩ (x ∈ N(g) ^ z ∈ DN(g))} where N is the number of vertices and E is the number of edges in the graph. The result for a subgraph g is the total number of elements in VT(g). |
[42]
|
Localized Modularity
| modularity |
| where |E| is the total number of edges. |
[49]
|
modified Vertex Distance Number
| modularity |
| d(i,j) is the length of the shortest path between vertices i and j. For this measure, i and j are all selected from V. |
-
|
Eigenvalues
| cycles |
| ER
j
is the real part of the j-th Eigenvalue for the adjacency matrix of the given subgraph. |
[50]
|
Subgraph Centrality
| cycles |
| A is the adjacency matrix. We computed SC for k [1,99]. |
[42]
|
Cyclic Coefficient
| cycles |
| S
i
is the smallest possible cycle of vertex i and two of its neighboring vertices k. The total Cyclic Coefficient for all vertices N is then given as θ |
[42]
|