Advance Practical PHP User-Defined Graph Structure - video 115X
We are going to look at the “Adjacency List” approach.
An adjacency list is a graph data structure representing a graph as a collection of unordered lists, where each list describes the neighbors of a specific vertex. It is implemented as an array or map, where each index (vertex) maps to a linked list, array, or dynamic list of connected vertices.
Analogy: Think of a roadmap where cities are vertices and the roads connecting them are edges. Social networks are also graphs (people are vertices, friendships are edges).
Key Feature: Unlike a tree, there are no restrictions on how nodes connect; they can form cycles, and a node can have any number of connections.
Types:
Directed: Edges have a direction (one-way street).
Undirected: Edges are bidirectional (two-way street).
Weighted: Edges have a cost or distance value (road length).
The structure is typically implemented in code using an Adjacency List (storing a list of neighbors for each vertex) or an Adjacency Matrix (using a 2D array to show if an edge exists between two vertices).
Let's implement a graph (adjacency list)
We'll use a class that manages a single associative array ($adjList) to store all the connections.
Key Takeaways
Feature Description Implementation Detail
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Vertices The individual data points (nodes). Stored as the keys in the $adjList associative array.
Edges The connections between vertices. Stored as values (arrays of neighboring vertices) associated with each key.
Flexibility Easily model different relationships (e.g., roads, social networks). Achieved by controlling the addEdge logic (unidirectional or bidirectional).
Why your PHP code is efficient:
Associative Arrays: Using isset($this adjList[$vertex]) allows for O(1) lookup time to check if a city already exists.
Dynamic Scaling: Your addVertex method ensures that the graph grows dynamically. You don't need to define the size of the "map" upfront.
Bidirectional Logic: By passing $undirected = true, you've correctly handled the symmetry required for a two-way road system.
A Quick "Pro-Tip" for your implementation:
If you were to use this for a massive dataset (like a real social network), you might want to prevent duplicate edges.
Currently, if you call $cityGraph addEdge("New York", "Chicago") twice, "Chicago" will appear twice in New York's neighbor list.
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