Definition of a Network Graph
A network graph is a fundamental mathematical structure consisting of points, known as nodes or vertices, and lines connecting them, called edges or links. It's used to visualize and analyze pairwise relationships or interactions between various entities within a system.
Key Components: Nodes and Edges
The two essential components are nodes, which represent individual entities (e.g., people, computers, cities), and edges, which symbolize the relationships or connections between these entities (e.g., friendships, data flow, roads). Edges can be directed (showing a one-way relationship), undirected (a mutual relationship), and can be assigned weights to indicate the strength, cost, or capacity of the connection.
A Practical Example: Social Media Connections
Consider a social media platform where each user is a node. If two users are friends, an undirected edge connects their respective nodes. If User A follows User B but User B does not follow User A, a directed edge would be drawn from A to B. The frequency of interaction or closeness of the relationship might be represented by a weight on that edge, such as a numerical value.
Importance and Diverse Applications
Network graphs are indispensable across numerous scientific and engineering disciplines. In computer science, they model communication networks, the structure of the internet, and data dependencies. Biologists use them to represent gene regulatory networks or neural connections in the brain. In social sciences, they are vital for analyzing social structures, information dissemination, and disease spread. Their versatility makes them powerful tools for understanding complex systems.