A vertex identifier (non-negative integer).

A directed edge from one vertex to another.

Takes vertex and outputs neighboring vertices. The Neighbors type is the function from a vertex to its neighbors

Map from edges to their sequential index (1-based). Used for edge-attribute lookup.

Graph definition of directed Graphs undirected graphs should include reverse edges.

Construct an Edge from a (source, target) tuple.

Convert an Edge to a (source, target) tuple.

Graph constructor given a neighbors function

Graph constructor given a list of edges.

Builds the adjacency map in a single O(E) pass using fromListWith, then wraps it in a closure for O(log V) neighbor lookup.

All edges of the graph, in EdgeMap key order.

Reverse the direction of an edge.

All edges of the graph with reversed direction.

Reverse all edges in the graph.

Get the subgraph of a graph by including vertices satisfying given predicate.

Get the subgraph of a graph by including edges satisfying given predicate.

Make a graph undirected by adding all missing reverse edges.

All outgoing edges from a vertex.

Enumerate all edges implied by a Neighbors function over a vertex set.

Build an explicit adjacency map from the graph's Neighbors closure.

Check whether an edge exists in the graph.

Gives the position of the edge to the edges list

Source vertex of an edge.

Target vertex of an edge.

Number of vertices in the graph.

Number of edges in the graph.

Make a graph directed by removing randomly reverse edges

Complete undirected graph from number of vertices