|
\(G=(\mathcal {V},\mathcal {E})\)
|
(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
|
