- What does a complete graph look like?
- How many cycles are in a complete graph?
- How can we represent a graph internally?
- What is a weighted graph?
- What does a complete graph mean?
- Is clique a complete graph?
- Does Dijkstra work for unweighted graphs?
- What is Dijkstra shortest path algorithm?
- What is weighted and unweighted graph?
- What is a weighted adjacency matrix?
- How do you find the shortest path in a weighted graph?

## What does a complete graph look like?

In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge.

A complete digraph is a directed graph in which every pair of distinct vertices is connected by a pair of unique edges (one in each direction)..

## How many cycles are in a complete graph?

Actually a complete graph has exactly (n+1)! cycles which is O(nn).

## How can we represent a graph internally?

Internally, it uses an adjacency list representation. A Vertex will represent a vertex in a directed graph; it is used internally by the Graph class. A Vertex contains a String representation of its name, and its adjacency list (as a LinkedList).

## What is a weighted graph?

A weighted graph is a graph in which each branch is given a numerical weight. A weighted graph is therefore a special type of labeled graph in which the labels are numbers (which are usually taken to be positive).

## What does a complete graph mean?

Definition: A complete graph is a graph with N vertices and an edge between every two vertices. ▶ There are no loops. ▶ Every two vertices share exactly one edge. We use the symbol KN for a complete graph with N vertices.

## Is clique a complete graph?

A complete graph is often called a clique. The size of the largest clique that can be made up of edges and vertices of G is called the clique number of G.

## Does Dijkstra work for unweighted graphs?

If there are no negative weight cycles, then we can solve in O(E + VLogV) time using Dijkstra’s algorithm. Since the graph is unweighted, we can solve this problem in O(V + E) time. … This algorithm will work even when negative weight cycles are present in the graph.

## What is Dijkstra shortest path algorithm?

Dijkstra’s algorithm (or Dijkstra’s Shortest Path First algorithm, SPF algorithm) is an algorithm for finding the shortest paths between nodes in a graph, which may represent, for example, road networks. … For a given source node in the graph, the algorithm finds the shortest path between that node and every other.

## What is weighted and unweighted graph?

If edges in your graph have weights then your graph is said to be a weighted graph, if the edges do not have weights, the graph is said to be unweighted. A weight is a numerical value attached to each individual edge. … An unweighted graph may be used because a relationship in terms of magnitude doesn’t exist.

## What is a weighted adjacency matrix?

The adjacency matrix of a weighted graph can be used to store the weights of the edges. If an edge is missing a special value, perhaps a negative value, zero or a large value to represent “infinity”, indicates this fact.

## How do you find the shortest path in a weighted graph?

One common way to find the shortest path in a weighted graph is using Dijkstra’s Algorithm. Dijkstra’s algorithm finds the shortest path between two vertices in a graph. It can also be used to generate a Shortest Path Tree – which will be the shortest path to all vertices in the graph (from a given source vertex).