From: Improving accuracy of expected frequency of uncertain roles based on efficient ensembling
Notation | Description |
---|---|
GÂ =Â (V, E) | Deterministic graph or backbone graph |
V, E | Sets of nodes and edges |
\(N = |V|,\,L = |E|\) | Numbers of nodes and edges |
g = (U, F) | Motif, or connected subgraph |
\({{\bar{d}}}=L/N\) | Average degree of each node |
\(\mathbf{R}, {{\mathcal {R}}}, {\bar{\mathbf{R}}}\) | R-dimensional vectors of N nodes, i.e., \(N \times R\) matrix |
R | Number of role patterns |
\(\mathbf{C}, {{\mathcal {C}}}, {\bar{\mathbf{C}}}\) | \(N \times N\) similarity matrix |
\(\mathbf{H}, {{\mathcal {H}}}, {\bar{\mathbf{H}}}\) | \(N \times K\) affiliation matrix |
K | Number of role clusters |
\(\varGamma (v)\) | Set of adjacent nodes of node v |
\({{\mathcal {G}}} = (G, \mathbf{p})\) | Uncertain graph |
p(e), p | Edge-existence probability |
\(G_s = (V, E_s)\) | Sampled graph of an uncertain graph |
S | Number of samples |
Pr[G] | Occurrence probability of graph G |
\(\delta ()\) | Kronecker delta function |
\({{\mathcal {D}}}_{s,s'}\) | Set of edges that appear in \(G_s\) but not in \(G_{s'}\), and vice versa. |