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<!DOCTYPE html>
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<title>dip::Graph class | DIPlib | a library for quantitative image analysis</title>
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<a href="https://diplib.org"><img src="DIPlib_logo.svg" alt="" />DIPlib</a><span class="m-breadcrumb">┃</span><a href="index.html" class="m-thin">a library for quantitative image analysis</a><span class="m-breadcrumb">┃</span><a href="https://github.com/DIPlib/diplib/releases/tag/3.5.2" class="m-thin">version 3.5.2</a> </span>
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<h1>
<div class="m-doc-include m-thin m-right-m m-text-right">
<a href="graphs.html" class="m-doc">Graphs</a> module<br/><span class="m-code m-thin">#include <a href="file--diplib--graph-h.html">"diplib/graph.h"</a></span> </div>
<span class="m-breadcrumb"><a href="dip.html">dip</a>::<wbr/></span>Graph <span class="m-thin">class</span> </h1>
<p>A non-directed, edge-weighted graph.</p>
<div class="m-block m-default">
<h3>Contents</h3>
<ul>
<li>
Reference
<ul>
<li><a href="#typeless-methods">Constructors, destructors, assignment and conversion operators</a></li>
<li><a href="#nested-classes">Classes</a></li>
<li><a href="#alias-members">Aliases</a></li>
<li><a href="#function-members">Functions</a></li>
</ul>
</li>
</ul>
</div>
<p>Vertices are identified by an index, these indices are expected to be consecutive. Each vertex contains a list
of indices to edges, and has an optional value.</p>
<p>Edges are represented by indices to two vertices, and a double precision floating-point weight.
Not all edges are actually used; use <a href="#dip-Graph-Edge-IsValid-C"><code>dip::Graph::Edge::IsValid</code></a> to test this.</p>
<section id="typeless-methods">
<h2>Constructors, destructors, assignment and conversion operators</h2>
<dl class="m-doc">
<dt id="dip-Graph-Graph-dip-uint--dip-uint-">
<span class="m-doc-wrap-bumper"><a href="#dip-Graph-Graph-dip-uint--dip-uint-" class="m-doc-self">Graph</a>(</span><span class="m-doc-wrap"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> nVertices,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> nEdges = 0) <span class="m-label m-flat m-info">explicit</span> </span>
</dt>
<dd>Construct a graph with <code>nVertices</code> vertices. Vertices are identified by their index, which
is in the range [0,<code>nVertices</code>]. <code>nEdges</code> is the expected number of edges for each vertex, and is used
to reserve space for them.</dd>
<dt>
<span class="m-doc-wrap-bumper"><a href="#dip-Graph-Graph-Image-CL-dip-uint--String-CL" class="m-doc">Graph</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& image,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 1,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& weights = "difference")</span>
</dt>
<dd>Construct a graph for the given image. <a href="#dip-Graph-Graph-Image-CL-dip-uint--String-CL">more...</a></dd>
</dl>
</section>
<section id="nested-classes">
<h2>Classes</h2>
<dl class="m-doc">
<dt>
struct <a href="dip-Graph-Vertex.html" class="m-doc">Vertex</a>
</dt>
<dd>A vertex in the graph</dd>
<dt>
struct <a href="#dip-Graph-Edge" class="m-doc">Edge</a>
</dt>
<dd>An edge in the graph <a href="#dip-Graph-Edge">more...</a></dd>
</dl>
</section>
<section id="alias-members">
<h2>Aliases</h2>
<dl class="m-doc">
<dt id="dip-Graph-VertexIndex">
using <a href="#dip-Graph-VertexIndex" class="m-doc-self">VertexIndex</a> = <a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a>
</dt>
<dd>Type for indices to vertices</dd>
<dt id="dip-Graph-EdgeIndex">
using <a href="#dip-Graph-EdgeIndex" class="m-doc-self">EdgeIndex</a> = <a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a>
</dt>
<dd>Type for indices to edges</dd>
<dt id="dip-Graph-EdgeList">
using <a href="#dip-Graph-EdgeList" class="m-doc-self">EdgeList</a> = std::vector<EdgeIndex>
</dt>
<dd>Type for list of edge indices</dd>
</dl>
</section>
<section id="function-members">
<h2>Functions</h2>
<dl class="m-doc">
<dt id="dip-Graph-NumberOfVertices-C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Graph-NumberOfVertices-C" class="m-doc-self">NumberOfVertices</a>(</span><span class="m-doc-wrap">) const -> <a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a></span>
</dt>
<dd>Returns the number of vertices in the graph.</dd>
<dt id="dip-Graph-NumberOfEdges-C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Graph-NumberOfEdges-C" class="m-doc-self">NumberOfEdges</a>(</span><span class="m-doc-wrap">) const -> <a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a></span>
</dt>
<dd>Returns the number of edges in the graph, including invalid edges.</dd>
<dt id="dip-Graph-CountEdges-C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Graph-CountEdges-C" class="m-doc-self">CountEdges</a>(</span><span class="m-doc-wrap">) const -> <a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a></span>
</dt>
<dd>Counts the number of valid edges in the graph.</dd>
<dt id="dip-Graph-Edges-C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Graph-Edges-C" class="m-doc-self">Edges</a>(</span><span class="m-doc-wrap">) const -> std::vector<Edge> const&</span>
</dt>
<dd>Gets the set of edges in the graph. The weights of the edges are mutable, they can be directly modified.
Not all edges connect vertices, use <a href="#dip-Graph-Edge-IsValid-C"><code>dip::Graph::Edge::IsValid</code></a> to test.</dd>
<dt id="dip-Graph-EdgeVertex-EdgeIndex--bool--C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Graph-EdgeVertex-EdgeIndex--bool--C" class="m-doc-self">EdgeVertex</a>(</span><span class="m-doc-wrap"><a href="dip-Graph.html#dip-Graph-EdgeIndex" class="m-doc">dip::Graph::EdgeIndex</a> edge,
bool which) const -> <a href="dip-Graph.html#dip-Graph-VertexIndex" class="m-doc">dip::Graph::VertexIndex</a></span>
</dt>
<dd>Gets the index to one of the two vertices that are joined by an edge.
<code>which</code> is 0 or 1 to specify which of the two vertices to return.</dd>
<dt id="dip-Graph-OtherVertex-EdgeIndex--VertexIndex--C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Graph-OtherVertex-EdgeIndex--VertexIndex--C" class="m-doc-self">OtherVertex</a>(</span><span class="m-doc-wrap"><a href="dip-Graph.html#dip-Graph-EdgeIndex" class="m-doc">dip::Graph::EdgeIndex</a> edge,
<a href="dip-Graph.html#dip-Graph-VertexIndex" class="m-doc">dip::Graph::VertexIndex</a> vertex) const -> <a href="dip-Graph.html#dip-Graph-VertexIndex" class="m-doc">dip::Graph::VertexIndex</a></span>
</dt>
<dd>Finds the index to the vertex that is joined to the vertex with index <code>vertex</code> through the edge with
index <code>edge</code>.</dd>
<dt id="dip-Graph-EdgeWeight-EdgeIndex--C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Graph-EdgeWeight-EdgeIndex--C" class="m-doc-self">EdgeWeight</a>(</span><span class="m-doc-wrap"><a href="dip-Graph.html#dip-Graph-EdgeIndex" class="m-doc">dip::Graph::EdgeIndex</a> edge) const -> <a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a>&</span>
</dt>
<dd>Returns a reference to the weight of the edge with index <code>edge</code>. This value is mutable even
if the graph is <code>const</code>.</dd>
<dt id="dip-Graph-IsValidEdge-EdgeIndex--C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Graph-IsValidEdge-EdgeIndex--C" class="m-doc-self">IsValidEdge</a>(</span><span class="m-doc-wrap"><a href="dip-Graph.html#dip-Graph-EdgeIndex" class="m-doc">dip::Graph::EdgeIndex</a> edge) const -> bool</span>
</dt>
<dd>Returns <code>true</code> if the edge is a valid edge.</dd>
<dt id="dip-Graph-EdgeIndices-VertexIndex--C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Graph-EdgeIndices-VertexIndex--C" class="m-doc-self">EdgeIndices</a>(</span><span class="m-doc-wrap"><a href="dip-Graph.html#dip-Graph-VertexIndex" class="m-doc">dip::Graph::VertexIndex</a> vertex) const -> <a href="dip-Graph.html#dip-Graph-EdgeList" class="m-doc">dip::Graph::EdgeList</a> const&</span>
</dt>
<dd>Get the indices to the edges that join vertex <code>vertex</code>.</dd>
<dt id="dip-Graph-VertexValue-VertexIndex--C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Graph-VertexValue-VertexIndex--C" class="m-doc-self">VertexValue</a>(</span><span class="m-doc-wrap"><a href="dip-Graph.html#dip-Graph-VertexIndex" class="m-doc">dip::Graph::VertexIndex</a> vertex) const -> <a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a>&</span>
</dt>
<dd>Returns a reference to the value of the vertex <code>vertex</code>. This value is mutable even if the graph is <code>const</code>.</dd>
<dt id="dip-Graph-AddVertex-dip-uint--dfloat-">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Graph-AddVertex-dip-uint--dfloat-" class="m-doc-self">AddVertex</a>(</span><span class="m-doc-wrap"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> nEdges = 0,
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> weight = 0.0) -> <a href="dip-Graph.html#dip-Graph-VertexIndex" class="m-doc">dip::Graph::VertexIndex</a></span>
</dt>
<dd>Adds a vertex to the graph with the given weight and space reserved for the given number of edges.
Returns the index to the new vertex.</dd>
<dt id="dip-Graph-AddEdge-VertexIndex--VertexIndex--dfloat-">
<span class="m-doc-wrap-bumper">void <a href="#dip-Graph-AddEdge-VertexIndex--VertexIndex--dfloat-" class="m-doc-self">AddEdge</a>(</span><span class="m-doc-wrap"><a href="dip-Graph.html#dip-Graph-VertexIndex" class="m-doc">dip::Graph::VertexIndex</a> vertex1,
<a href="dip-Graph.html#dip-Graph-VertexIndex" class="m-doc">dip::Graph::VertexIndex</a> vertex2,
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> weight)</span>
</dt>
<dd>Add an edge between vertices <code>vertex1</code> and <code>vertex2</code>, with weight <code>weight</code>. If the edge already exists,
update the weight of the edge to be <code>weight</code>.</dd>
<dt id="dip-Graph-AddEdgeSumWeight-VertexIndex--VertexIndex--dfloat-">
<span class="m-doc-wrap-bumper">void <a href="#dip-Graph-AddEdgeSumWeight-VertexIndex--VertexIndex--dfloat-" class="m-doc-self">AddEdgeSumWeight</a>(</span><span class="m-doc-wrap"><a href="dip-Graph.html#dip-Graph-VertexIndex" class="m-doc">dip::Graph::VertexIndex</a> vertex1,
<a href="dip-Graph.html#dip-Graph-VertexIndex" class="m-doc">dip::Graph::VertexIndex</a> vertex2,
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> weight)</span>
</dt>
<dd>Add an edge between vertices <code>vertex1</code> and <code>vertex2</code>, with weight <code>weight</code>. If the edge already exists,
update the weight of the edge by adding <code>weight</code> to the existing weight.</dd>
<dt id="dip-Graph-DeleteEdge-VertexIndex--VertexIndex-">
<span class="m-doc-wrap-bumper">void <a href="#dip-Graph-DeleteEdge-VertexIndex--VertexIndex-" class="m-doc-self">DeleteEdge</a>(</span><span class="m-doc-wrap"><a href="dip-Graph.html#dip-Graph-VertexIndex" class="m-doc">dip::Graph::VertexIndex</a> vertex1,
<a href="dip-Graph.html#dip-Graph-VertexIndex" class="m-doc">dip::Graph::VertexIndex</a> vertex2)</span>
</dt>
<dd>Delete the edge between vertices <code>vertex1</code> and <code>vertex2</code>.</dd>
<dt id="dip-Graph-DeleteEdge-EdgeIndex-">
<span class="m-doc-wrap-bumper">void <a href="#dip-Graph-DeleteEdge-EdgeIndex-" class="m-doc-self">DeleteEdge</a>(</span><span class="m-doc-wrap"><a href="dip-Graph.html#dip-Graph-EdgeIndex" class="m-doc">dip::Graph::EdgeIndex</a> edge)</span>
</dt>
<dd>Delete the edge <code>edge</code>.</dd>
<dt id="dip-Graph-Neighbors-VertexIndex-">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Graph-Neighbors-VertexIndex-" class="m-doc-self">Neighbors</a>(</span><span class="m-doc-wrap"><a href="dip-Graph.html#dip-Graph-VertexIndex" class="m-doc">dip::Graph::VertexIndex</a> vertex) -> std::vector<VertexIndex></span>
</dt>
<dd>Returns a list of indices to neighboring vertices. The list is created. <code>EdgeIndices</code> is
a more efficient, but less convenient, function.</dd>
<dt id="dip-Graph-UpdateEdgeWeights-T-F--C">
<div class="m-doc-template">template<typename F></div>
<span class="m-doc-wrap-bumper">void <a href="#dip-Graph-UpdateEdgeWeights-T-F--C" class="m-doc-self">UpdateEdgeWeights</a>(</span><span class="m-doc-wrap">F func) const</span>
</dt>
<dd>Re-computes edge weights using the function <code>func</code>, called as <code>dfloat func(dfloat val1, dfloat val2)</code>,
where the two inputs to <code>func</code> are the value of the two vertices.</dd>
<dt id="dip-Graph-UpdateEdgeWeights-C">
<span class="m-doc-wrap-bumper">void <a href="#dip-Graph-UpdateEdgeWeights-C" class="m-doc-self">UpdateEdgeWeights</a>(</span><span class="m-doc-wrap">) const</span>
</dt>
<dd>Re-computes edge weights as the absolute difference between vertex values.</dd>
<dt id="dip-Graph-MinimumSpanningForest-std-vector<VertexIndex>-CL-C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-Graph-MinimumSpanningForest-std-vector<VertexIndex>-CL-C" class="m-doc-self">MinimumSpanningForest</a>(</span><span class="m-doc-wrap">std::vector<VertexIndex> const& roots = {}) const -> <a href="dip-Graph.html" class="m-doc">dip::Graph</a></span>
</dt>
<dd>Computes the minimum spanning forest (MSF) using Prim’s algorithm.
See <a href="graphs.html#dip-MinimumSpanningForest-Graph-CL-std-vector<Graph-VertexIndex>-CL"><code>dip::MinimumSpanningForest</code></a> for details. Does not modify `<em>this</em>.</dd>
<dt>
<span class="m-doc-wrap-bumper">void <a href="#dip-Graph-RemoveLargestEdges-dip-uint-" class="m-doc">RemoveLargestEdges</a>(</span><span class="m-doc-wrap"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> number)</span>
</dt>
<dd>Removes <code>number</code> edges with the largest weights from the graph. <a href="#dip-Graph-RemoveLargestEdges-dip-uint-">more...</a></dd>
</dl>
</section>
<section>
<h2>Class documentation</h2>
<section class="m-doc-details" id="dip-Graph-Edge"><div>
<h3>
struct <a href="#dip-Graph-Edge" class="m-doc-self">Edge</a>
</h3>
<p>An edge in the graph</p>
<p>If both vertices are 0, the edge is not valid (never used or deleted). Otherwise, <code>vertices[0] < vertices[1]</code>.</p>
<table class="m-table m-fullwidth m-first-tight m-flat m-doc">
<thead><tr><th>Variables</th><th></th></tr></thead>
<tbody>
<tr>
<td>
std::array<VertexIndex, 2> <a href="#dip-Graph-Edge-vertices" class="m-doc-self" id="dip-Graph-Edge-vertices">vertices</a> </td>
<td>
The two vertices joined by this edge
</td>
</tr>
<tr>
<td>
mutable <a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> <a href="#dip-Graph-Edge-weight" class="m-doc-self" id="dip-Graph-Edge-weight">weight</a> </td>
<td>
The weight of this edge
</td>
</tr>
</tbody>
</table>
</div></section>
</section>
<section>
<h2>Function documentation</h2>
<section class="m-doc-details" id="dip-Graph-Graph-Image-CL-dip-uint--String-CL"><div>
<h3>
<span class="m-doc-wrap-bumper">
</span><span class="m-doc-wrap"><span class="m-doc-wrap-bumper"><a href="#dip-Graph-Graph-Image-CL-dip-uint--String-CL" class="m-doc-self">Graph</a>(</span><span class="m-doc-wrap"><a href="dip-Image.html" class="m-doc">dip::Image</a> const& image,
<a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> connectivity = 1,
<a href="supporttypes.html#dip-String" class="m-doc">dip::String</a> const& weights = "difference")</span></span>
</h3>
<p>Construct a graph for the given image.</p>
<p>Each pixel becomes a vertex in the graph, the vertex’s index is equal to the linear index (see <a href="dip-Image.html#pointers">On pixel coordinates, indices, offsets and data pointers</a>)
of the pixel in the image (that is, vertices are stored in the same order as the pixels in the image with
normal strides). Vertex values are set to the corresponding pixel value.</p>
<p>An edge will connect each pixel to each of its neighbors.</p>
<p><code>connectivity</code> indicates which pixels are considered neighbors. Currently, only a connectivity of 1 is
allowed. This makes neighbors the pixels at a city-block distance of 1 (in 2D, there are 4 such neighbors,
in 3D there are 6).</p>
<p>The value of <code>weights</code> is:
- <code>"difference"</code> (default): the edge weights are given by the absolute difference between the two pixel values.
- <code>"average"</code>: the edge weights are given by the average of the two pixel values.
- <code>"zero"</code>: the edge weights are all set to 0, use <a href="dip-Graph.html#dip-Graph-UpdateEdgeWeights-T-F--C"><code>dip::Graph::UpdateEdgeWeights</code></a> to compute weights in some other way,
or manually set the weights.</p>
</div></section>
<section class="m-doc-details" id="dip-Graph-RemoveLargestEdges-dip-uint-"><div>
<h3>
<span class="m-doc-wrap-bumper">void
</span><span class="m-doc-wrap"><span class="m-doc-wrap-bumper"><a href="#dip-Graph-RemoveLargestEdges-dip-uint-" class="m-doc-self">RemoveLargestEdges</a>(</span><span class="m-doc-wrap"><a href="supporttypes.html#dip-uint" class="m-doc">dip::uint</a> number)</span></span>
</h3>
<p>Removes <code>number</code> edges with the largest weights from the graph.</p>
<p>If the graph is a minimum spanning tree, it will be converted to a minimum spanning forest with
<code>number + 1</code> trees. This is a segmentation of the tree into the <code>number + 1</code> regions with smallest
trees.</p>
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