Prepare a graph-first geodesic-MDS path cache

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")
)

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.

Value

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

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.

The all-pairs distance_matrix contains symmetric strict graph distances. Retained-route lengths in pair_graph_distance follow the deterministic near-tie path convention and can differ slightly from these targets. Route selection and path diagnostics are not changed by this distinction.

Examples

cycle_edges <- edges.cycle(6)
prepared <- prepare.graph.geodesic.mds(cycle_edges, n = 6)