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Table 1 Symbols and definitions

From: SURREAL: Subgraph Robust Representation Learning

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