List vs Matrix

The Idea

Two ways to store the same graph. An adjacency list keeps, per node, only the neighbours it actually has — small when edges are scarce. An adjacency matrix reserves a cell for every possible pair, so "is A joined to B?" is one lookup, but blanks dominate.

Real-World Example

Football analysts log who passed to whom. Storing an eleven-by-eleven grid is fine, and instant to query, but scale it to every player in a league and almost every cell reads zero. Per-player pass lists hold the same information in a fraction of the space.

The Code

players = ["GK", "DF", "MF", "FW"]
passes = [("GK", "DF"), ("DF", "MF"), ("MF", "FW"), ("MF", "DF")]

adj = {p: [] for p in players}          # adjacency list
for a, b in passes:
    adj[a].append(b)                    # directed: a passed to b

idx = {p: i for i, p in enumerate(players)}
mat = [[0] * len(players) for _ in players]   # adjacency matrix
for a, b in passes:
    mat[idx[a]][idx[b]] = 1

print(adj["MF"])                        # ['FW', 'DF']
print(mat[idx["MF"]])                   # [0, 1, 0, 1]

adj = {"MF": [], "FW": []}
adj["MF"].___("FW")     # record the pass MF -> FW
print(adj["MF"])        # ['FW']