prepare.graph.geodesic.mds: Prepare a graph-first geodesic-MDS path cache

Description

prepare.graph.geodesic.mds() prepares the full all-pairs chosen geodesic cache for an arbitrary connected weighted graph. This is the graph-first entry point corresponding to the manuscript's definition of GMDS on a connected weighted graph together with a chosen geodesic family \((G, \Gamma)\).

Usage

prepare.graph.geodesic.mds(
  edges = NULL,
  n = NULL,
  adj_list = NULL,
  weight_list = NULL,
  edge_weights = NULL,
  tie_mode = c("single", "average")
)

Value

A prepared object with class "grip_gmds_prepared" layered on top of the existing full geodesic path-cache structure.

Arguments

edges: Two-column integer matrix of edges (1-based vertex ids).
n: Number of vertices. If omitted with adj_list, defaults to length(adj_list). If omitted with edges, defaults to max(edges).
adj_list: Adjacency list (1-based) for an undirected graph.
weight_list: Optional parallel list of positive edge weights.
edge_weights: Optional positive edge-weight vector parallel to edges.
tie_mode: Shortest-path aggregation mode. "single" uses one deterministic chosen shortest path per pair. "average" replaces each tied shortest-path family by the exact uniform average over all shortest paths between the pair.

Details

The graph can be supplied either as an edge list plus parallel weights or as an adjacency-list representation. The returned object stores the all-pairs graph distances, the chosen shortest-path family, and the flattened edge-path cache reused by the GMDS scorer and optimizer.