Add crate doc front-page, and update readme

README.md

@@ -1,8 +1,63 @@
 # grapherity
 
-Library for graph models and algorithms.
+Graph models and algorithms.
 
-This library is still experimental and its API may therefore change frequently.
+This crate provides data structures to model graphs and to perform algorithms on these data structures. The functionality presented is designed to be easy to use, flexible, and performant.
+
+Currently supported are:
+
+* Undirected graph types `Graph` and `AppendGraph`, built on a flat, index-based adjacency list,
+* Maps to freely associate custom data with vertices and edges, 
+* Connectivity and pathing algorithms: Dijkstra's algorithm, DFS, and BFS in different variants,
+* Exposed traits to implement custom graph data structures or algorithms.
+
+For more information, see the [documentation](https://docs.rs/grapherity/latest/grapherity/).
+
+## Example
+
+```
+// Brings commonly used traits into scope.
+use grapherity::prelude::*;
+use grapherity::models::Graph;
+use grapherity::algorithms;
+
+let mut graph = Graph::new();
+// Creates a map for edge weights with a default weight.
+let mut weights = graph.edge_map(1);
+// Adds three vertices and two edges.
+let v1 = graph.add_vertex();
+let v2 = graph.add_vertex();
+let v3 = graph.add_vertex();
+graph.add_edge(v1, v2);
+let e = graph.add_edge(v2, v3);
+// Sets a non-default weight for the second edge.
+weights[e] = 5;
+
+// Checks the number of vertices.
+assert_eq!(graph.vertex_count(), 3);
+// Checks the number of edges.
+assert_eq!(graph.edge_count(), 2);
+// Checks that v1 and v2 are adjacent.
+assert!(graph.are_adjacent(v1, v2));
+// Checks that v1 and v3 are not adjacent.
+assert!(!graph.are_adjacent(v1, v3));
+// Checks the sum of all vertex degrees.
+let sum: usize = graph.vertices().map(|v| graph.degree(v)).sum();
+assert_eq!(sum, 1 + 2 + 1);
+
+// Calls Dijkstra's algorithm using the edge weights to find the shortest path from v1 to v3.
+let result = algorithms::dijkstra(&graph, v1, |e| weights[e]);
+assert_eq!(result.distances[v3], Some(1 + 5));
+assert_eq!(result.predecessors[v3], Some(v2));
+
+// Deletes the middle vertex and its incident edges.
+graph.delete_vertex(v2);
+
+// Calls Dijkstra's algorithm again on the now disconnected graph.
+let result = algorithms::dijkstra(&graph, v1, |e| weights[e]);
+assert_eq!(result.distances[v3], None);
+assert_eq!(result.predecessors[v3], None);
+```
 
 ## License