Generated from the survey's 81 tagged papers (1,297 verified
facet tags). Heat = paper count; a dashed tile is an open direction. Click any tile
for its papers.
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The role view mirrors the journal paper's role taxonomy: hover a row
label for what the role means. Year range inside each tile = first–latest paper.
Generalizing the node distribution π (a realized open direction)
Structural entropy is the expected code length of a random walker localized by an encoding tree. Standard SE hard-codes the walker's stationary distribution as π_v = d_v/2m (degree, or PageRank for directed graphs). A natural, mostly-unexplored generalization is to let π be GIVEN exogenously (a query/importance/prior distribution unrelated to edge weights). Interpretation: it IS meaningful exactly when π is the stationary distribution of SOME walk on the graph — e.g. a teleporting / personalized-PageRank walk with teleport vector p, or a Metropolis–Hastings walk engineered to have stationary π. Then SE = bits to encode that p-biased walker, giving 'query-biased / personalized structural entropy'. An arbitrary π with no underlying process loses the code-length reading but remains a well-defined importance-weighted partition functional (a rate-distortion / non-uniform-source view). Directed-graph SE already does a special case of this (π = PageRank ≠ degree); the general 'bring-your-own-π' SE is the open frontier.
Open directions surfaced by the table
Signed-graph structural entropy: no work found — the +/- semantics need a sign-aware cut/volume (e.g. frustration-weighted).
Bipartite structural entropy: touched only implicitly (a hypergraph-SE recommender on the user-item bipartite graph) — no dedicated two-sided volume / co-clustering encoding-tree definition.
Hypergraph SE beyond a single recommendation application: community detection, pooling and RL on hypergraphs are open.
Directed SE for deep learning: pooling / structure-learning / RL on directed graphs barely touched (only EDEN).
Dynamic SE for graph learning / RL: incremental SE exists for detection, not yet as a differentiable pooling or exploration signal.
EXOGENOUS node distribution pi: SE almost always fixes pi = d_v/2m (or PageRank for directed). Letting pi be a GIVEN importance/query distribution unrelated to edge weight is essentially unexplored (see note).
Data-driven from the survey's facet tags (results/facet_tags.jsonl); a blank
tile means no paper in the corpus was tagged there (not proof of non-existence). Empty
columns for signed and bipartite graphs, and sparse hypergraph / directed rows,
map the frontier.