Graph theory

▸ Placing the vertices…

▸ Connecting edges & counting degrees

▸ Loading the Seven Bridges of Königsberg

▸ Calibrating Euler · BFS/DFS · coloring

▸ Building the spanning tree & bipartite graph

▸ Ready — Online. ✅

Structure & metrics

🕸️ Sample graph

number of odd-degree vertices

Vertices |V|—

Edges |E|—

Odd-degree vertices—

Maximum degree—

Eulerian path?—

Colors (χ)—

Tip

Each dot is a vertex, each line is an edge. The number on a vertex's shoulder = its degree (green = even, red = odd). Traversing every edge "in one stroke" (an Eulerian path) is only possible with 0 or 2 odd-degree vertices.

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Click a vertex to see its degree · pick a scenario on the right to run an algorithm

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|V| · |E| · odd-degree vertex count over time |E||V|odd vertices