- 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).