A periodic table of structural-entropy methods

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. ← benchmark · gallery · tutorial · more maps · survey

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

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.