Build a Graph as an Adjacency List

Represent an undirected graph as a per-vertex list of neighbours. For every edge (u, v), append v to adj[u] and u to adj[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.rb

edges = [[1, 2], [1, 3], [2, 4], [3, 4], [4, 5], [5, 6]]
adj = {}
edges.each do |u, v|
	adj[u] ||= []
	adj[v] ||= []
	adj[u] << v
	adj[v] << u
end
parts = []
adj.keys.sort.each do |v|
	parts << "#{v}: [#{adj[v].join(", ")}]"
end
puts "{" + parts.join(", ") + "}"

Complexity

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

Implementation notes

Ruby: a Hash maps each vertex to an Array of neighbours; keys are sorted before printing for a stable order.
The replay shows the adjacency list after each edge is added, matching the lesson spec.

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