What is an undirected graph?

An undirected graph is a graph in which edges have no direction.

Formally: A graph G = (V, E), where each edge is an unordered pair of vertices {u, v}. This means the connection between u and v is mutual: u ↔ v.

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#Main idea

If vertices are connected, movement is possible in both directions. That is, the edge {A, B} means a connection both as A → B and B → A at the same time.

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#Example

If there are vertices A, B, C, and edges:

• A-B,
• B-C, then you can go from A to C and back, through B.

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#Typical applications

• Friendship on social networks (both added each other).
• Roads between cities, if traffic is two-way.
• Interaction networks, where the connection is mutual.

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Summary: in an undirected graph, all connections are two-way, direction does not matter.