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graphs
dlegland edited this page Aug 25, 2025
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The graphs module of the MatGeom library provides functions to easily create, process and display geometric graphs (geometric in the sense that nodes are associated to geometric position in 2D or 3D). Manipulation of vertex list or edges may require functions from the geom2d module.
Graph data structure is represented by at least two arrays:
- NODES, which contains coordinates of each vertex
- EDGES, which contains indices of start and end vertex.
Others arrays may sometimes be used:
- FACES, which contains indices of vertices of each face (either a double array, or a cell array)
- CELLS, which contains indices of faces of each cell.
An alternative representation is to use a struct, containing at least the two fields:
- 'nodes'
- 'edges' corresponding to the data described above.
The topological description of 2D graph is entirely contained in EDGES array, and the NODES array is used only to display the graph.
Caution: this type of data structure is easy to create and to manage, but may be very inefficient for some algorithms.
Graphs are usually considered as non-oriented in this package.
delaunayGraph - Graph associated to Delaunay triangulation of input points
euclideanMST - Build euclidean minimal spanning tree of a set of points
prim_mst - Minimal spanning tree by Prim's algorithm
knnGraph - Create the k-nearest neighbors graph of a set of points
relativeNeighborhoodGraph - Relative Neighborhood Graph of a set of points
gabrielGraph - Gabriel Graph of a set of points
voronoi2d - Compute a voronoi diagram as a graph structure
boundedVoronoi2d - Return a bounded voronoi diagram as a graph structure
centroidalVoronoi2d - Centroidal Voronoi tesselation within a polygon
boundedCentroidalVoronoi2d - Create a 2D Centroidal Voronoi Tesselation in a box
cvtUpdate - Update germs of a CVT with given points
cvtIterate - Update germs of a CVT using random points with given density
imageGraph - Create equivalent graph of a binary image
imageBoundaryGraph - Get boundary of image as a graph
adjacencyListToEdges - Convert an adjacency list to an edge array.
pruneGraph - Remove all edges with a terminal vertex
mergeGraphs - Merge two graphs, by adding nodes, edges and faces lists.
grMergeNodes - Merge two (or more) nodes in a graph.
grMergeMultipleNodes - Simplify a graph by merging multiple nodes
grMergeMultipleEdges - Remove all edges sharing the same extremities
grSimplifyBranches - Replace branches of a graph by single edges
grMean - Compute mean from neihgbours
grMedian - Compute median from neihgbours
grDilate - Morphological dilation on graph
grErode - Morphological erosion on graph
grClose - Morphological closing on graph
grOpen - Morphological opening on graph
grShortestPath - Find a shortest path between two nodes in the graph
grPropagateDistance - Propagates distances from a vertex to other vertices
grVertexEccentricity - Eccentricity of vertices in the graph
graphDiameter - Diameter of a graph
graphPeripheralVertices - Peripheral vertices of a graph
graphCenter - Center of a graph
graphRadius - Radius of a graph
grFindGeodesicPath - Find a geodesic path between two nodes in the graph
grFindMaximalLengthPath - Find a path that maximizes sum of edge weights
grEdgeLengths - Compute length of edges in a geometric graph
grMergeNodeClusters - Merge cluster of connected nodes in a graph
grMergeNodesMedian - Replace several nodes by their median coordinate
clipGraph - Clip a graph with a rectangular area
clipGraphPolygon - Clip a graph with a polygon
addSquareFace - Add a (square) face defined from its vertices to a graph
grFaceToPolygon - Compute the polygon corresponding to a graph face
graph2Contours - Convert a graph to a set of contour curves
grNodeDegree - Degree of a node in a (undirected) graph
grNodeInnerDegree - Inner degree of a node in a graph
grNodeOuterDegree - Outer degree of a node in a graph
grAdjacentNodes - Find list of nodes adjacent to a given node
grAdjacentEdges - Find list of edges adjacent to a given node
grOppositeNode - Return opposite node in an edge
grLabel - Associate a label to each connected component of the graph
grRemoveNode - Remove a node in a graph
grRemoveNodes - Remove several nodes in a graph
grRemoveEdge - Remove an edge in a graph.
grRemoveEdges - Remove several edges from a graph
drawGraph - Draw a graph, given as a set of vertices and edges
drawGraphEdges - Draw edges of a graph
fillGraphFaces - Fill faces of a graph
drawDigraph - Draw a directed graph, given as a set of vertices and edges
drawDirectedEdges - Draw edges with arrow indicating direction
drawEdgeLabels - Draw values associated to graph edges
drawNodeLabels - Draw values associated to graph nodes
drawSquareMesh - Draw a 3D square mesh given as a graph
patchGraph - Transform 3D graph (mesh) into a patch handle
readGraph - Read a graph from a text file
writeGraph - Write a graph to an ascii file