# API for clojure.algo.graph - Basic graph theory algorithms0.1.0 (in development)

by Jeffrey Straszheim

Full namespace name: clojure.algo.graph

## Overview

`Basic graph theory algorithms`

## Public Variables and Functions

function
```Usage: (add-loops g)
```
`For each node n, add the edge n->n if not already present.`

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## component-graph

function
```Usage: (component-graph g)
(component-graph g sccs)
```
```Given a graph, perhaps with cycles, return a reduced graph that is acyclic.
Each node in the new graph will be a set of nodes from the old.
These sets are the strongly connected components.  Each edge will
be the union of the corresponding edges of the prior graph.```

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## dependency-list

function
```Usage: (dependency-list g)
```
```Similar to a topological sort, this returns a vector of sets. The
set of nodes at index 0 are independent.  The set at index 1 depend
on index 0; those at 2 depend on 0 and 1, and so on.  Those withing
a set have no mutual dependencies.  Assume the input graph (which
much be acyclic) has an edge a->b when a depends on b.```

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## fixed-point

function
```Usage: (fixed-point data fun max equal)
```
```Repeatedly apply fun to data until (equal old-data new-data)
returns true.  If max iterations occur, it will throw an
exception.  Set max to nil for unlimited iterations.```

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## get-neighbors

function
```Usage: (get-neighbors g n)
```
`Get the neighbors of a node.`

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## lazy-walk

function
```Usage: (lazy-walk g n)
(lazy-walk g ns v)
```
```Return a lazy sequence of the nodes of a graph starting a node n.  Optionally,
provide a set of visited notes (v) and a collection of nodes to
visit (ns).```

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## post-ordered-nodes

function
```Usage: (post-ordered-nodes g)
```
`Return a sequence of indexes of a post-ordered walk of the graph.`

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## recursive-component?

function
```Usage: (recursive-component? g ns)
```
`Is the component (recieved from scc) self recursive?`

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## remove-loops

function
```Usage: (remove-loops g)
```
`For each node n, remove any edges n->n.`

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## reverse-graph

function
```Usage: (reverse-graph g)
```
```Given a directed graph, return another directed graph with the
order of the edges reversed.```

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## scc

function
```Usage: (scc g)
```
```Returns, as a sequence of sets, the strongly connected components
of g.```

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## self-recursive-sets

function
```Usage: (self-recursive-sets g)
```
```Returns, as a sequence of sets, the components of a graph that are
self-recursive.```

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## stratification-list

function
```Usage: (stratification-list g1 g2)
```
```Similar to dependency-list (see doc), except two graphs are
provided.  The first is as dependency-list.  The second (which may
have cycles) provides a partial-dependency relation.  If node a
depends on node b (meaning an edge a->b exists) in the second
graph, node a must be equal or later in the sequence.```

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## transitive-closure

function
```Usage: (transitive-closure g)
```
```Returns the transitive closure of a graph.  The neighbors are lazily computed.

Note: some version of this algorithm return all edges a->a
regardless of whether such loops exist in the original graph.  This
version does not.  Loops will be included only if produced by
cycles in the graph.  If you have code that depends on such
behavior, call (-> g transitive-closure add-loops)```

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