degreeSequence
Each vertex's degree, largest first (a loop counts twice; for a directed graph, in plus out).
g(network) --
Graph Theory
isGraphical
Whether a simple graph with these degrees exists (the Erdos-Gallai test).
degrees(array) --
eulerKind
Whether a walk can use every edge exactly once: euler circuit (closed), euler path (open) or neither. Vertices with no edges are ignored.
g(network) --
eulerPath
A walk over every edge exactly once, as a list of vertices, or a sentence if there is none. An open walk starts at an odd vertex.
g(network) --
hamiltonPath
A path through every vertex exactly once, or a sentence if there is none. An exact search: up to 24 vertices.
g(network) --
hamiltonCycle
A cycle through every vertex exactly once, or a sentence if there is none. The first vertex is not repeated at the end of the list. An exact search: up to 24 vertices.
g(network) --
graphColouring
The chromatic number and a colouring with that many colours (fields chromatic_number and colours, numbered from 0). An exact search: up to 24 vertices; refused for a vertex joined to itself.
g(network) --
net
Creates a graph-theory network with n vertices (undirected by default, or directed).
n(number) -- number of verticesdirected(boolean) -- optional, defaults to false
edge
Adds an edge between two vertices, addressed by 0-based index (unweighted by default, or with an explicit weight).
g(network) --u(number) -- vertex indexv(number) -- vertex indexweight(number) -- optional, defaults to 1.0
node
Places a vertex at explicit (x, y) coordinates, required before dijkstra() can trace the graph.
g(network) --i(number) -- vertex indexx(number) --y(number) --
dijkstra
Traces Dijkstra's shortest-path algorithm from a source vertex, optionally to a destination, producing a step-by-step event trace for visualization. Every vertex must already have an explicit position via node().
g(network) --src(number) -- source vertex indexdst(number) -- optional destination vertex index
bfs
Breadth-first search order from a start vertex.
g(network) --src(integer) --
dfs
Depth-first search order from a start vertex.
g(network) --src(integer) --
distances
Shortest distances from a start vertex to every vertex (Dijkstra; inf where unreachable).
g(network) --src(integer) --
shortestPath
The vertices of a shortest path from src to dst, in order.
g(network) --src(integer) --dst(integer) --
bellmanFord
Shortest distances and predecessors from a start vertex, allowing negative edge weights (an error on a negative cycle).
g(network) --src(integer) --
minSpanningTree
A minimum spanning tree's edges (Prim's algorithm).
g(network) --
kruskal
A minimum spanning tree's edges (Kruskal's algorithm).
g(network) --
topologicalSort
An order of the vertices of a directed acyclic graph in which every edge points forward.
g(network) -- directed
components
The connected components, each as a list of vertices.
g(network) --
isConnected
True if every vertex can reach every other.
g(network) --
hasCycle
True if the graph contains a cycle.
g(network) --
isBipartite
True if the vertices split into two groups with every edge between the groups.
g(network) --
numVertices
The number of vertices.
g(network) --
numEdges
The number of edges.
g(network) --
neighbors
The vertices joined to v by an edge.
g(network) --v(integer) --
hasEdge
True if there is an edge from u to v.
g(network) --u(integer) --v(integer) --
edgeWeight
The weight of the edge from u to v, or text if there is none.
g(network) --u(integer) --v(integer) --
adjacencyMatrix
The adjacency matrix: edge weights (1 when unweighted), 0 on the diagonal, inf where there is no edge.
g(network) --