Graphs are the foundation of any coding interview. As a result, it is critical to have a solid understanding of this subject. But don't be concerned about any of it. Ninjas are here to help, and today we'll talk about different types of graphs and their applications.
A graph is represented by a series of dots that represent vertices (V) and are connected by lines or curves that represent edges (E).
Now let's discuss different types of graphs.
A graph is known as finite if it has a finite number of vertices and edges.
A graph is known as infinite if it has an infinite number of vertices and edges.
A graph is known astrivial if it has only one vertex and no edges.
A simple graph is one that comprises not more than one edge between two vertices. A set of railway tracks that connects two cities is an example of a simple graph.
A null graph is a graph that consists only of isolated vertices.
A simple graph with 'N' vertices is known as complete graph if the degree of each vertex is N - 1, implying that one vertex is connected by N - 1 edges. Full Graph is another name for a complete graph.
A pseudo graph is a graph G with a self-loop and multiple edges.
A simple graph is known as regular if all of its vertices have the same degree. All complete graphs are regular, but the opposite is not true.
A bipartite graph (or bigraph) contains vertices that may be divided into two distinct and independent sets, {U} and {V}, with each edge connecting a vertex in {U} to one in {V}. A bipartite graph, on the other hand, is one that contains no odd-length cycles.
The two sets, {U} and {V}, can be compared to a two-color coloring of the graph: if all nodes in {U} are blue and all nodes in {V} are green, each edge will have endpoints of different colors, as required by the graph coloring problem.
Set representation
Bipartite Graph
A labeled graph is one in which the vertices and edges of a graph are labeled with a name, data, or weight. It is also known as a Weighted Graph.
A digraph is a graph G = (V, E) with a mapping f that translates every edge onto an ordered pair of vertices (Vi, Vj). It is also referred to as a Directed Graph. An ordered pair is an edge between Vi and Vj with an arrow pointing from Vi to Vj (Vi, Vj).
A subgraph of a graph G(V, E) is one in which V1(G) is a subset of V(G) and E1(G) is a subset of E(G), and each edge of G1 has the same end vertices as in G.
A graph is known as a connected graph if there is a path from any vertex 'U' to any vertex 'V' or vice versa.
If there is no path between any two vertices in a graph, it is said to be disconnected.
Graphs that form cycles are called cyclic graphs.
Any graph which contains some parallel edges but doesn’t contain any self-loop is called a multigraph.
But, What are the applications of Graphs?
Graphs are used to describe communication networks, data organization, computing equipment, and so on. Graph theory is also utilized in chemistry and physics to investigate molecules. Graph theory is also used extensively in sociology. Graphs are useful in geometry and some sections of topology, such as knot theory. Graph theory has applications in biology and conservation as well.
Check out this problem - No of Spanning Trees in a Graph
In this article, we have extensively discussed the types of Graphs along with their applications. We hope that this blog has helped you enhance your knowledge of Graphs, and if you would like to learn more, check out our articles on Library. Do upvote our blog to help other ninjas grow. Happy Coding!
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