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Graph and Network Algorithms

Directed and undirected graphs, network analysis

Graphs model the connections in a network and are widely applicable to a variety of physical, biological, and information systems. You can use graphs to model the neurons in a brain, the flight patterns of an airline, and much more. The structure of a graph is comprised of “nodes” and “edges”. Each node represents an entity, and each edge represents a connection between two nodes. For more information, see Directed and Undirected Graphs.

Example plots of undirected and directed graphs


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graphGraph with undirected edges
digraphGraph with directed edges
addnodeAdd new node to graph
rmnodeRemove node from graph
addedgeAdd new edge to graph
rmedgeRemove edge from graph
flipedgeReverse edge directions
numnodesNumber of nodes in graph
numedgesNumber of edges in graph
findnodeLocate node in graph
findedgeLocate edge in graph
edgecountNumber of edges between two nodes
reordernodesReorder graph nodes
subgraphExtract subgraph
centralityMeasure node importance
conncompConnected graph components
biconncompBiconnected graph components
condensationGraph condensation
bctreeBlock-cut tree graph
toposortTopological order of directed acyclic graph
isdagDetermine if graph is acyclic
transreductionTransitive reduction
transclosureTransitive closure
isisomorphicDetermine whether two graphs are isomorphic
isomorphismCompute isomorphism between two graphs
ismultigraphDetermine whether graph has multiple edges
simplifyReduce multigraph to simple graph
bfsearchBreadth-first graph search
dfsearchDepth-first graph search
shortestpathShortest path between two single nodes
shortestpathtreeShortest path tree from node
distancesShortest path distances of all node pairs
allpathsFind all paths between two graph nodes (Since R2021a)
maxflowMaximum flow in graph
minspantreeMinimum spanning tree of graph
hascyclesDetermine whether graph contains cycles (Since R2021a)
allcyclesFind all cycles in graph (Since R2021a)
cyclebasisFundamental cycle basis of graph (Since R2021a)
adjacencyGraph adjacency matrix
incidenceGraph incidence matrix
laplacianGraph Laplacian matrix
degreeDegree of graph nodes
neighborsNeighbors of graph node
nearestNearest neighbors within radius
indegreeIn-degree of nodes
outdegreeOut-degree of nodes
predecessorsNode predecessors
successorsNode successors
inedgesIncoming edges to node
outedgesOutgoing edges from node
plotPlot graph nodes and edges
labeledgeLabel graph edges
labelnodeLabel graph nodes
layoutChange layout of graph plot
highlightHighlight nodes and edges in plotted graph


GraphPlotGraph plot for directed and undirected graphs


GraphPlot PropertiesGraph plot appearance and behavior


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