Graph theory introduction. Part 1
Published: 2023-05-14 11:27:07

## What are graphs?
In computer science, a graph is a way to represent connections or relationships between objects. It consists of a set of nodes or vertices, which are connected by edges or links. Each edge represents a connection between two nodes.

The vertices and edges can have properties such as name, label, id, etc. Edges can also have direction and weight as property.

Graphs are a way of visualizing or representing connections between objects.

## Applications of graph theory
Graphs are used in various applications such as social networks, routing algorithms, image processing, and more. They can be represented visually as diagrams or through mathematical models, and can be analyzed to gain insights into the relationships between the nodes. Some elaboration upon the application of graph theory in various fields: -

- Social Networks: Social networks such as Facebook, Twitter, and LinkedIn are examples of graphs, where each person is a node, and the edges represent relationships such as friendships or follows. Graph theory algorithms can be used to analyze the structure of social networks, identify influential people, detect communities, and predict user behavior.

- Transportation Networks: Transportation networks, such as road networks, airline routes, and public transportation systems, can be represented as graphs. Graph theory algorithms can be used to optimize routes, calculate shortest paths, and identify bottlenecks.

- Image Processing: Images can be represented as graphs, where nodes represent pixels, and edges represent relationships such as spatial proximity or color similarity. Graph theory algorithms can be used to segment images, identify objects, and remove noise.

- Biology: Many biological systems can be modeled as graphs, such as protein interaction networks, metabolic pathways, and food webs. Graph theory algorithms can be used to analyze these systems, identify key components, and predict their behavior.

- Operations Research: Graph theory is used extensively in operations research to model and optimize processes such as scheduling, resource allocation, and project management.

## Types of graph
In graph theory, there are several types of graphs, each with their own characteristics and properties. Some of the most common types or graphs are: -

- Undirected Graph: An undirected graph is a graph where the edges have no direction or orientation. That is, each edge connects two nodes, but it does not specify a "starting" or "ending" node. In an undirected graph, each edge is considered to be bidirectional.

- Directed Graph: A directed graph is a graph where each edge has a direction or orientation. That is, each edge connects a starting node to an ending node, and it cannot be reversed. In a directed graph, each edge is considered to be unidirectional.

- Weighted Graph: A weighted graph is a graph where each edge is assigned a numerical value or weight. The weight can represent a cost, distance, or any other attribute associated with the edge. Weighted graphs are often used to model real-world systems, such as transportation networks.

- Bipartite Graph: A bipartite graph is a graph where the nodes can be divided into two disjoint sets such that no two nodes in the same set are connected by an edge. Bipartite graphs are often used to represent relationships between two different types of objects, such as employees and projects.

- Complete Graph: A complete graph is a graph where each pair of nodes is connected by an edge. That is, a complete graph has the maximum possible number of edges for a given number of nodes. Complete graphs are often used to model dense relationships, such as in social networks.

- Planar Graph: A planar graph is a graph that can be drawn on a plane without any edges crossing each other. Planar graphs are often used to model spatial relationships, such as in circuit design or cartography.

- Tree: A tree is a connected graph with no cycles. That is, there is exactly one path between any two nodes in a tree. Trees are often used to represent hierarchical structures, such as file systems or family trees.

## Some common graph algorithms
Here, we will only name them and elaborate upon some of them in next part of the blog.

- Breadth-First-Search
- Depth-First-Search
- Dijkstra's algorithm
- Bellman-Ford algorithm
- Kruskal's algorithm
- Prim's algorithm

To use graph as databases you can use PostgreSQL's extension Apache AGE: -
More about apache age here: https://age.apache.org/
Github here: https://github.com/apache/age/