Graphs: relationships as data and algorithms

A graph is relationships as data: nodes connected by edges. Social networks, task dependencies, citations, money moving between accounts, products bought together — all are naturally graphs, and questions like "what's the shortest path?" or "who is most connected?" are awkward on a table but native to a graph.

In plain Python you can store a directed weighted graph as a dict of dicts: graph[u][v] = weight means an edge from u to v. Building that structure from an edge list is enough for many course exercises; specialised libraries exist, but the idea does not depend on them.

graph = {}
for u, v, w in edges:
    graph.setdefault(u, {})[v] = w

Shortest path on non-negative weights is Dijkstra: keep the best known distance to each node, and always expand the closest unsettled node next. Centrality and connected components are the same idea at larger scale: walk the adjacency data instead of joining tables.