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vignettes/subgraphs.Rmd

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The `spdep` package has always been careful about disconnected graphs, especially where the disconnected observations are graph nodes with no neighbours, that is no incoming or outgoing edges. In `nb` neighbour objects, they are encoded as integer vectors of length 1 containing integer `0`, which is an invalid index on $[1, N]$, where $N$ is the observation count. Functions taking neighbour objects as arguments use the `zero.policy` argument to guide how to handle no-neighbour observations.
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`spdep` has also had `n.comp.nb` to find the number of disjoint connected subgraphs in an `nb` object, contributed by Nicholas Lewin-Koh in 2001 and using depth-first search for symmetric neighbours, showing in addition which observations belong to which subgraph. Obviously, no-neighbour observations are singleton graph nodes, but subgraphs are also troubling for spatial analysis, because there is no connection between the spatial processes in those subgraphs. The ripples in one pond cannot cross into a separate pond if they are not connected.
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`spdep` has also had `n.comp.nb` to find the number of disjoint connected subgraphs in an `nb` object, contributed by Nicholas Lewin-Koh in 2001 and using depth-first search for symmetric neighbours, showing in addition which observations belong to which subgraph. Obviously, no-neighbour observations are singleton graph nodes, but subgraphs are also troubling for spatial analysis, because there is no connection between the spatial processes in those subgraphs. **The ripples in one pond cannot cross into a separate pond if they are not connected**.
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From `spdep` 1.3-1, steps began to raise awareness of the possibility that neighbour objects might be created that are disconnected in some way, mostly through warnings, and through the computation of subgraph measures by default. This vignette is intended to provide some background to these steps.
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