How can graph algorithms represent cities highways and social networks?

In computer science, graph theory provides a powerful framework for modeling complex systems by representing them as a set of vertices (nodes) connected by edges (lines).12

Representing Cities and Highways

To model transportation networks, vertices typically represent locations such as cities or intersections, while edges represent the roads or highways connecting them.32
* Weights: In these models, edges are often assigned a weight—such as distance, travel time, or cost—to represent the "length" of the route.3
* Optimization: Computer scientists use these weighted graphs to solve optimization problems, such as finding the shortest path between two cities or determining the most efficient route for a delivery vehicle to visit multiple locations, a classic challenge known as the traveling-salesman problem.13

Representing Social Networks

Social networks are represented by treating individuals as vertices and their relationships (such as friendships or professional connections) as edges.1
* Directed Graphs: When relationships are one-way (e.g., following someone on social media), the network is modeled as a directed graph, where edges have a specific direction.13
* Analysis: By analyzing the structure of these graphs, algorithms can identify influential nodes, community clusters, or the shortest path of connection between two people.12