Table 1 Symbols and definitions
Symbol | Definition |
|---|---|
\(G=(\mathcal {V},\mathcal {E})\) | (Un)weighted and undirected graph |
\(\mathcal {V}, |\mathcal {V}|=\) n | Set and number of vertices (nodes), respectively |
\(\mathcal {E}, |\mathcal {E}|=\) m | Set and number of links (edges), respectively |
G ′ | Modified graph after adding node z |
\(\mathcal {N}\)(u) | Set of direct neighbors of node u, i.e., nodes connected to u |
NE(u) | Expanded neighborhood of node u |
NR(u) | Refined neighborhood of node u |
EX | Set of expanded nodes that will form NE(u) (initialized to {u}) |
P | Set of pending nodes, initialized to u’s neighbors, \(\mathcal {N}\)(u) |
W uv | Weight of an edge (u,v) \(\in \mathcal {E}\) |
V u | Voltage of node u |
deg(u) | Weighted degree of node u |
f G | Mapping function |
f(u) | Feature representation of node u |
D(u,v) | Distance between nodes u and v |
C(v,w) | Weight/Conductance of the edge connecting nodes v and w |
I(s,t) | Current flows between nodes s and t in the NE(u) |
Pr(NR(u) ∣f(u) | Probability of observing the refined neighborhood of u given its feature representation |
d | Dimensionality of learned representation |
α | Scalar; penalty parameter |
MAXE, MAXR | Desired size of NE(u) and NR(u), respectively |
z | Universal sink node |
c | Nearest common neighbor of non-neighboring nodes u and v |
w | A node that belongs to NR(u) |
\(\mathbb {R}\) | Set of real numbers |
NLP | Natural language processing |
CBOW | Continuous bag of words |
SE | Spatio-electric |