Table 1 Definitions of the topological parameters used in the network analysis
Statistical characteristic | Symbol | Equation a |
|---|---|---|
Degree | k | \( {k}_i=\sum \limits_{j=1}^N{e}_{ij} \) |
Average degree | <k> | \( <k>=\frac{1}{N}{\sum}_{i=1}^N{k}_i \) |
Average path length | L | \( L=\frac{1}{N\left(N-1\right)}\sum \limits_{i\ne j}{d}_{ij} \) |
Diameter | D | D = max {dij} |
Node strength | s | \( {s}_i=\sum \limits_{j\in {N}_i}{w}_{ij} \) |
Dispersion of weight distribution | Y | \( {Y}_i=\sum \limits_{j\in {N}_i}{\left[\frac{w_{ij}}{s_i}\right]}^2 \) |
Degree centrality | Cd | \( {C}_d=\frac{k_i}{N-1} \) |
Betweenness centrality | Cb | \( {C}_b=\sum \limits_{j\left(<k\right)}^N\sum \limits_k^N\frac{g_{jk}(i)}{g_{jk}} \) |
Closeness centrality | Cc | \( {C}_c=\frac{N-1}{\sum \limits_{j=1}^N{d}_{ij}} \) |