Table 1.

DRN metrics and their interpretations (adapted from [50]⁠).

Metric	Equation	Interpretation
Averaged degree centrality	$\overline{{\mathit{DC}}_i}=\frac{1}{m\left(n-1\right)}{\sum }_{k=1}^m{\sum }_{j=1,j\ne i}^n{A}_{\mathit{ijk}}$	Aijk is the adjacency from the 3D tensor consisting of a time series of adjacencies Aij from adjacency matrices A. It is the averaged connectivity around a residue i. The number of frames is denoted by m. A residue is more central if it has a high local connectivity.
Averaged betweenness centrality	$\overline{{\mathit{BC}}_v}=\frac{1}{m}{\sum }_{i=1}^m{\sum }_{s,t\in V}\frac{{\sigma }_i\left(s,t|v\right)}{{\sigma }_i\left(s,t\right)}$	BC measures the fraction of all s-t node pairs that traverse a given node v along their geodesic distance. σi(s,t|v) denotes the number of paths bridged by residue v, while σi(s,t) is the total number of paths for the graph, both evaluated at time i. For each residue, this value is then averaged from the total m frames.
Averaged farness	$L_v=\frac{1}{m(n-1)}{\sum }_{i=1}^m{\sum }_{u=1}^{n-1}{d}_i\left(u,v\right)$	The farness (at time i) for a node v is the sum of its geodesic distance di to every other node u, normalised by the number of residues. The higher this number, the longer the distance to be travelled to reach other nodes of the network graph.
Averaged closeness centrality	$\overline{{\mathit{CC}}_v}=\frac{n-1}{m}{\sum }_{i=1}^m{\sum }_{u=1}^{n-1}\frac{1}{d_i\left(v,u\right)}$	Closeness is the inverse of farness and is maximised when the latter is smallest. In other words, a node would have a high closeness when its geodesics to every other node are shortest.
Averaged eigencentrality	$A\mathit{·}\overrightarrow{EC}=\lambda ·\overrightarrow{EC}$ (Eq. i) $\overline{{\mathit{EC}}_i}=\frac{1}{m}{\sum }_{k=1}^m{\mathit{EC}}_{\mathit{ik}}$ (Eq. ii)	Eigencentrality is an extension of degree centrality. It assigns node importance by solving for the dominant unit eigenvector EC of the adjacency matrix A. Eq. i shows the eigenvector decomposition method that can be used to determine EC. In NetworkX, EC is solved using the power iteration method. In Eq. ii, the averaged EC for residue i is determined from the time average from m frames. The converged eigenvector is a metric that recursively assigns importance, giving high centrality to nodes that have a high degree or to those connected to high importance nodes.
Averaged Katz centrality	${\mathit{KC}}_i=\alpha {\sum }_{j=1}^n{A}_{\mathit{ij}}{\mathit{KC}}_j+\beta$ (Eq. i) $\overline{{\mathit{KC}}_i}=\frac{1}{m}{\sum }_{k=1}^m{\mathit{KC}}_{\mathit{ik}}$ (Eq. ii)	KC is a generalization of EC, which via two constants, namely an adjacency damping coefficient α and a basal adjacency β, assigns a centrality on the basis of a node’s immediate connectivity. While β avoids adjacencies of zero, α weighs the magnitude of each centrality value. Node centrality can be dampened to various extents – larger values of α make KC tend towards EC.
Averaged PageRank	${\mathit{PR}}_i=\alpha {\sum }_{j=1}^n\frac{A_{\mathit{ij}}}{D_j}{\mathit{PR}}_j+\beta$ (Eq. i) $\overline{{\mathit{PR}}_i}=\frac{1}{m}{\sum }_{k=1}^m{\mathit{PR}}_{\mathit{ik}}$ (Eq. ii)	PR is an adjusted version of KC, which also assigns node centrality based on that of their neighbors. For each round of the power iteration, the centrality of each neighbor to a node is normalised by its own degree D (given the graph is undirected), and each of the resulting neighbors' centrality is summed up and assigned to the parent node. As in KC, it also includes a damping factor α and a constant β.
Averaged eccentricity	$\overline{{\mathit{ECC}}_j}=\frac{1}{m}{\sum }_{i=1}^m{\mathit{max}}_{j,k\in V}{d}_i\left(j,k\right)$	ECC is the longest path from a node to any other node in a graph.