Build a Graph as an Adjacency List

Represent an undirected graph as a per-vertex list of neighbours. For every edge (u, v), record v as a neighbour of u and u as a neighbour of v. Neighbour lists keep insertion order so the graph is a stable, deterministic fixture for the search lessons.

Algorithm

The canonical fixture is 6 vertices [1..6] with undirected edges (1,2), (1,3), (2,4), (3,4), (4,5), (5,6) inserted in that order. The final adjacency list is {1: [2, 3], 2: [1, 4], 3: [1, 4], 4: [2, 3, 5], 5: [4, 6], 6: [5]}. This same graph drives graph-bfs, graph-dfs, and graph-shortest-path-bfs.

Basic Implementation

basic.R

edges <- list(c(1, 2), c(1, 3), c(2, 4), c(3, 4), c(4, 5), c(5, 6))
adj <- list()
for (e in edges) {
	u <- as.character(e[1])
	v <- as.character(e[2])
	adj[[u]] <- c(adj[[u]], e[2])
	adj[[v]] <- c(adj[[v]], e[1])
}
parts <- character(0)
for (v in 1:6) {
	key <- as.character(v)
	parts[length(parts) + 1] <- paste0(v, ": [", paste(adj[[key]], collapse = ", "), "]")
}
cat("{", paste(parts, collapse = ", "), "}\n", sep = "")

Complexity

Build: O(V + E)
Space: O(V + E)

Implementation notes

R: a named list() keyed by character vertex stores neighbour vectors; vertices 1..6 are printed in order.
The replay shows the adjacency list as the edges are processed, matching the lesson spec.

adjacency list Each edge adds two directed entries, one in each direction.