Build a Graph as an Adjacency List

Represent an undirected graph as a map from each vertex to its 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.

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

Visual walkthrough

The graph fixture is pinned once, then the adjacency list writes each undirected edge in both directions.

Step 1 - Pinned graph fixture

The six vertices and six undirected edges are the shared fixture for BFS and DFS.

Step 2 - Final adjacency list

Each row lists neighbours in the same insertion order used by the lesson.

Basic Implementation

                            basic.js
                        

                            const edges = [[1, 2], [1, 3], [2, 4], [3, 4], [4, 5], [5, 6]];
const adj = new Map();
for (const [u, v] of edges) {
    if (!adj.has(u)) adj.set(u, []);
    if (!adj.has(v)) adj.set(v, []);
    adj.get(u).push(v);
    adj.get(v).push(u);
}
const parts = [];
for (const [v, nbrs] of adj) {
    parts.push(v + ": [" + nbrs.join(", ") + "]");
}
console.log("{" + parts.join(", ") + "}");

                        

Complexity

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

Implementation notes

JavaScript: a Map keyed by vertex preserves insertion order, and each entry is an array of neighbours appended in edge order.
The replay shows the adjacency map after each edge is added, matching the lesson spec.