Data.Graph.Analysis.Algorithms.Common

Defines algorithms that work on both undirected and directed graphs.

Graph decomposition

Finding connected components.

Whilst the FGL library does indeed have a function components that returns the connected components of a graph, it returns each component as a list of Nodes. This implementation instead returns each component as a graph, which is much more useful.

Connected components are found by choosing a random node, then recursively extracting all neighbours of that node until no more nodes can be removed.

Note that for directed graphs, these are known as the weakly connected components.

componentsOf :: DynGraph g => g a b -> [g a b]

Find all connected components of a graph.

pathTree :: DynGraph g => Decomp g a b -> [NGroup]

Find all possible paths from this given node, avoiding loops, cycles, etc.

Clique Detection

Clique detection routines. Find cliques by taking out a node, and seeing which other nodes are all common neighbours (by both pre and suc).

cliquesIn :: DynGraph g => g a b -> [[LNode a]]

Finds all cliques (i.e. maximal complete subgraphs) in the given graph.

cliquesIn' :: DynGraph g => g a b -> [NGroup]

Finds all cliques in the graph, without including labels.

findRegular :: Graph g => g a b -> [[Node]]

Find all regular subgraphs of the given graph.

isRegular :: Graph g => g a b -> NGroup -> Bool

Determines if the list of nodes represents a regular subgraph.

Cycle Detection

Cycle detection. Find cycles by finding all paths from a given node, and seeing if it reaches itself again.

cyclesIn :: DynGraph g => g a b -> [LNGroup a]

Find all cycles in the given graph.

cyclesIn' :: DynGraph g => g a b -> [NGroup]

Find all cycles in the given graph, returning just the nodes.

uniqueCycles :: DynGraph g => g a b -> [LNGroup a]

Find all cycles in the given graph, excluding those that are also cliques.

uniqueCycles' :: DynGraph g => g a b -> [NGroup]

Find all cycles in the given graph, excluding those that are also cliques.

Chain detection

A chain is a path in a graph where for each interior node, there is exactly one predecessor and one successor node, i.e. that part of the graph forms a "straight line". Furthermore, the initial node should have only one successor, and the final node should have only one predecessor. Chains are found by recursively finding the next successor in the chain, until either a leaf node is reached or no more nodes match the criteria.

chainsIn :: (DynGraph g, Eq b) => g a b -> [LNGroup a]

Find all chains in the given graph.

chainsIn' :: (DynGraph g, Eq b) => g a b -> [NGroup]

Find all chains in the given graph.