Version 5.0 The LEDA User Manual

list BFS(const graph& G, node s, node array& dist,
node array& pred)
performs a bread first search as described above and computes for every
node v the predecessor edge pred[v] in the bfs shortest path tree. (You can
use the function COMPUTE SHORTEST PATH to extract paths from
the tree (cf. Section 12.2).)
int
COMPONENTS(const graph& G, node array& compnum)
COMPONENTS takes a graph G(V, E) as argument and computes the
connected components of the underlying undirected graph, i.e., for every
node v ∈ V an integer compnum[v] from [0 . . . c−1] where c is the number
of connected components of G and v belongs to the i-th connected component
iff compnum[v] = i. COMPONENTS returns c. The algorithm
([58]) has running time O(|V | + |E|).
int
STRONG COMPONENTS(const graph& G, node array& compnum)
STRONG COMPONENTS takes a directed graph G(V, E) as argument
and computes for every node v ∈ V an integer compnum[v] from [0 . . . c−
1] where c is the number of strongly connected components of G and v
belongs to the i-th strongly connected component iff compnum[v] = i.
STRONG COMPONENTS returns c. The algorithm ([58]) has running
time O(|V | + |E|).
int BICONNECTED COMPONENTS(const graph& G,
edge array& compnum)
BICONNECTED COMPONENTS computes the biconnected components
of the undirected version of G. A biconnected component of an
undirected graph is a maximal biconnected subgraph and a biconnected
graph is a graph which cannot be disconnected by removing one of its
nodes. A graph having only one node is biconnected.
Let c be the number of biconnected component and let c ′ be the number
of biconnected components containing at least one edge, c−c ′ is the number
of isolated nodes in G, where a node v is isolated if is not connected
to a node different from v (it may be incident to self-loops). The function
returns c and labels each edge of G (which is not a self-loop) by an integer
in [0 . . . c ′ − 1]. Two edges receive the same label iff they belong to the
same biconnected component. The edge labels are returned in compnum.
Be aware that self-loops receive no label since self-loops are ignored when
interpreting a graph as an undirected graph.
The algorithm ([21]) has running time O(|V | + |E|).