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