A graph in which each edge has a numerical value associated with it.

A graph in which each vertex has a numerical value associated with it.

A graph in which each edge has a color associated with it.

A graph in which each vertex has a color associated with it.

A matrix that represents the edges of a graph.

A matrix that represents the vertices of a graph.

A matrix that represents the weights of the edges of a graph.

A matrix that represents the degrees of the vertices of a graph.

A path between two vertices in a graph with the smallest total weight.

A path between two vertices in a graph with the largest total weight.

A path between two vertices in a graph with the smallest number of edges.

A path between two vertices in a graph with the largest number of edges.

Dijkstra's algorithm

Prim's algorithm

Kruskal's algorithm

Floyd-Warshall algorithm

O(V^2)

O(E log V)

O(V log V)

O(E)

Dijkstra's algorithm

Prim's algorithm

Kruskal's algorithm

Floyd-Warshall algorithm

O(V^2)

O(E log V)

O(V log V)

O(E)

Dijkstra's algorithm

Prim's algorithm

Kruskal's algorithm

Floyd-Warshall algorithm

O(V^2)

O(E log V)

O(V log V)

O(E)

In a weighted graph, each edge has a numerical value associated with it, while in an unweighted graph, each edge has a weight of 1.

In a weighted graph, each vertex has a numerical value associated with it, while in an unweighted graph, each vertex has a weight of 1.

In a weighted graph, each edge has a color associated with it, while in an unweighted graph, each edge has a color of black.

In a weighted graph, each vertex has a color associated with it, while in an unweighted graph, each vertex has a color of black.

In a directed weighted graph, the edges have a direction, while in an undirected weighted graph, the edges do not have a direction.

In a directed weighted graph, the vertices have a direction, while in an undirected weighted graph, the vertices do not have a direction.

In a directed weighted graph, the edges have a color, while in an undirected weighted graph, the edges do not have a color.

In a directed weighted graph, the vertices have a color, while in an undirected weighted graph, the vertices do not have a color.

In a simple weighted graph, each pair of vertices is connected by at most one edge, while in a multigraph, each pair of vertices can be connected by multiple edges.

In a simple weighted graph, each vertex has a degree of at most 1, while in a multigraph, each vertex can have a degree greater than 1.

In a simple weighted graph, each edge has a weight of 1, while in a multigraph, each edge can have a different weight.

In a simple weighted graph, each vertex has a color, while in a multigraph, each vertex can have a different color.

In a weighted graph, the edges have weights, while in a network, the edges have capacities.

In a weighted graph, the vertices have weights, while in a network, the vertices have capacities.

In a weighted graph, the edges have colors, while in a network, the edges have labels.

In a weighted graph, the vertices have colors, while in a network, the vertices have labels.

In a weighted graph, the edges have weights, while in a matroid, the edges have ranks.

In a weighted graph, the vertices have weights, while in a matroid, the vertices have ranks.

In a weighted graph, the edges have colors, while in a matroid, the edges have labels.

In a weighted graph, the vertices have colors, while in a matroid, the vertices have labels.