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A detailed tutorial on mathematical bridges. Step by step tutorial including several examples of mathematical bridges for reference.

The bridge is a type of mathematical structure. When an edge is taken off of a connected graph, and the resulting graph is disconnected, that edge is considered to be a bridge. Either way, the resulting graph is called a subgraph. The name “bridge” was thought up for these edges because they connect one part of the structure to another part of the structure, and are extremely important in a graph.

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A detailed tutorial on how to identify disconnected graphs. Step by step tutorial including several examples of disconnected graphs for reference.

A disconnected graph is a graph where not every single vertex is connected to all other vertices. Typically, graphs will have paths from all vertices, but if there is not a direct path from each and every vertex, then it is considered to be a disconnected graph. Some common shapes that are seen that are disconnected graphs are stars, rectangles, and hexagons. The opposite of a disconnected graph is a connected graph.

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A detailed tutorial on how to identify connected graphs. Step by step tutorial including several examples of connected graphs for reference.

A connected graph is a graph where every single vertex is connected to every other vertex. This does not mean to simply have a clear path from one vertex to another – it means there needs to be a direct path, or an edge, between two vertices. A triangle is a commonly seen shape that is a connected graph. The opposite of a connected graph is a disconnected graph.