Table 2.
The complete set of twenty-five standard and LOUD metrics, calculated at each node v
| Name | Details |
|---|---|
| Degree | Number of neighbours of v |
| Local clustering | Proportion of pairs of neighbours of v which are also connected |
| Redundancy | (Local clustering) × (Degree - 1) [43] |
| PageRank | Calculated with the default damping factor d=0.85 [45] |
| Closeness | Reciprocal to the sum over all u of node-to-node distances d(u,v) [46] |
| Harmonic centrality | The sum over all u of 1/d(u,v) [47] |
| Betweenness | Measures how many shortest paths a node v contributes to [46] |
| eone(v) | Number of edges in the step-one ego-network of v |
| ntwo(v) | Number of nodes in the step-two ego-network of v |
| ndiff(v) | Number of nodes that have exactly distance two to v |
| nsqdiff(v) | A measure of relative local density calculated as ntwo(v)−degree(v)2 |
| nratio(v) | The ratio of step-one to step-two neighbourhood sizes for v |
| LOUD Average local clustering | f(G) is the average local clustering |
| LOUD Global clustering | f(G) is the global clustering, i.e. the proportion of connected triplets of nodes which form triangles |
| LOUD Average redundancy | f(G) is the average redundancy |
| LOUD Average closeness | f(G) is the average closeness |
| LOUD Average path length | f(G) is the average path length |
| LOUD Number of connected pairs | f(G) is the number of pairs of nodes, which are in the same connected component |
| LOUD Average betweenness | f(G) is the average betweenness |
| LOUD Natural connectivity | f(G) is the natural connectivity [44] |
| LOUD Average eone(v) | f(G) is the average eone(v) |
| LOUD Average ntwo(v) | f(G) is the average ntwo(v) |
| LOUD Average ndiff(v) | f(G) is the average ndiff(v) |
| LOUD Average nsqdiff(v) | f(G) is the average nsqdiff(v) |
| LOUD Average nratio(v) | f(G) is the average nratio(v) |
Standard metrics are above the line break. LOUD metrics are below the line break. LOUD metrics are based on global metrics f calculated both for each thresholded network G, and for the same network, where in turn each node v has been isolated from its neighbours Gv. The difference between the two metrics is recorded as fLOUD(v)=f(G)−f(Gv)