Boundary (graph theory)

Short description: Graph nodes linked to, but not part of, a subgraph

In graph theory, the outer boundary of a subset S of the vertices of a graph G is the set of vertices in G that are adjacent to vertices in S, but not in S themselves. The inner boundary is the set of vertices in S that have a neighbor outside S. The edge boundary is the set of edges with one endpoint in the inner boundary and one endpoint in the outer boundary.[1]

These boundaries and their sizes are particularly relevant for isoperimetric problems in graphs, separator theorems, minimum cuts, expander graphs, and percolation theory.

## References

1. ↑ Benjamini, Itai (2013), Coarse geometry and randomness: École d'Été de Probabilités de Saint-Flour XLI – 2011, Lect. Notes Math., 2100, Cham: Springer, p. 2, doi:10.1007/978-3-319-02576-6, ISBN 978-3-319-02575-9

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