Pathfinding Algorithms (BFS, DFS)
Explore algorithms like Breadth-First Search and Depth-First Search to find paths and connections in a graph.
Pathfinding Algorithms (BFS, DFS) is a free Neo4j Graph Database Fundamentals lesson on CoddyKit — lesson 1 of 4. You can read the complete lesson below for free — then practise it hands-on in the browser with a built-in code editor and a 24/7 AI tutor. It is part of the Neo4j Graph Database Fundamentals learning path, one of 4 lessons in the course, and your progress syncs across the web and the CoddyKit app.
Finding Your Way in Graphs
Graphs are all about connections! Imagine a map where cities are points and roads are lines. Finding the best route from one city to another is a classic "pathfinding" problem.
In this lesson, we'll explore two fundamental algorithms for finding paths in graphs: Breadth-First Search (BFS) and Depth-First Search (DFS).
What's a Graph? Quick Review
Before we dive into algorithms, let's quickly review what a graph is:
- Nodes: These are the entities or points in your graph (e.g., people, cities, products).
- Relationships: These are the connections between nodes (e.g., "FRIENDS_WITH", "LOCATED_IN").
- Path: A sequence of connected nodes and relationships from one node to another.
BFS: Exploring Layer by Layer
Breadth-First Search (BFS) is like exploring a maze by checking all immediate exits from your current room, then all exits from those rooms, and so on.
It systematically explores a graph level by level, ensuring it finds the shortest path in terms of the number of relationships between two nodes (in an unweighted graph).
How BFS Works
BFS uses a "queue" (like a line at a store: first-in, first-out) to keep track of which nodes to visit next.
- It starts at a given node.
- It visits all its direct neighbors first.
- Then, it visits all the unvisited neighbors of those neighbors.
- It keeps track of visited nodes to avoid loops and redundant work.
BFS Code Example
Let's see a simple Python example of BFS on a small graph. We represent the graph using a dictionary where keys are nodes and values are lists of their neighbors.
def bfs_path(graph, start_node):
visited = []
queue = [start_node]
visited.append(start_node)
path = []
while queue:
current_node = queue.pop(0) # Get first node
path.append(current_node)
for neighbor in graph[current_node]:
if neighbor not in visited:
visited.append(neighbor)
queue.append(neighbor)
return path
if __name__ == "__main__":
# A simple graph:
# A -- B
# | |
# C -- D
graph_data = {
'A': ['B', 'C'],
'B': ['A', 'D'],
'C': ['A', 'D'],
'D': ['B', 'C']
}
print("BFS path from 'A':")
print(bfs_path(graph_data, 'A'))DFS: Diving Deep
Depth-First Search (DFS) takes a different approach. Instead of exploring layer by layer, it goes as deep as possible along each branch before backtracking.
Think of it as navigating a maze by always picking one path and following it to its end. If it's a dead end, you backtrack and try another path.
How DFS Works
DFS typically uses a "stack" (last-in, first-out) or recursion to manage its exploration.
- It starts at a given node.
- It picks one unvisited neighbor and moves to it.
- It repeats this process, going deeper into the graph.
- If it hits a dead end or a visited node, it backtracks to the last node with unvisited neighbors.
DFS Code Example
Here's a Python example for DFS. We'll use a recursive approach, which naturally uses the call stack to achieve depth-first traversal.
def dfs_path(graph, start_node, visited=None, path=None):
if visited is None:
visited = set()
if path is None:
path = []
visited.add(start_node)
path.append(start_node)
for neighbor in graph[start_node]:
if neighbor not in visited:
dfs_path(graph, neighbor, visited, path)
return path
if __name__ == "__main__":
# A simple graph:
# A -- B
# | |
# C -- D
graph_data = {
'A': ['B', 'C'],
'B': ['A', 'D'],
'C': ['A', 'D'],
'D': ['B', 'C']
}
print("DFS path from 'A':")
# Note: DFS path can vary based on neighbor order
print(dfs_path(graph_data, 'A'))BFS vs. DFS: Key Differences
BFS and DFS are both powerful, but they suit different problems:
- BFS: Guarantees the shortest path (in terms of relationships). Great for finding the closest friends, nearest locations.
- DFS: Useful for checking connectivity, finding all paths, or topological sorting. Can be more memory efficient for very deep graphs.
- Memory: BFS can use more memory for wide graphs (many neighbors). DFS can use more stack space for deep graphs.
Quick Check: Pathfinding Choice
You're building a social network feature that needs to find the shortest connection (fewest friends) between two users. Which algorithm would be most suitable for this task in an unweighted graph?
Recap & Next Steps
Great job! In this lesson, you've learned about the two fundamental graph traversal algorithms:
- Breadth-First Search (BFS): Explores layer by layer, good for shortest paths.
- Depth-First Search (DFS): Dives deep, useful for checking connectivity or finding all paths.
Understanding these algorithms is key to solving many graph problems and will help you appreciate how graph databases efficiently find connections.
Frequently asked questions
Is the “Pathfinding Algorithms (BFS, DFS)” lesson free?
Yes — the full text of “Pathfinding Algorithms (BFS, DFS)” is free to read here on the web, and the Neo4j Graph Database Fundamentals course includes 4 lessons in total. To practise it interactively (a built-in code editor and a 24/7 AI tutor) and unlock the rest of the Neo4j Graph Database Fundamentals course, upgrade to CoddyKit PRO.
What will I learn in “Pathfinding Algorithms (BFS, DFS)”?
Explore algorithms like Breadth-First Search and Depth-First Search to find paths and connections in a graph. You practise Neo4j Graph Database Fundamentals with hands-on code you run directly in the browser, and a 24/7 AI tutor answers your questions as you work through the lesson.
Do I need any experience to start Neo4j Graph Database Fundamentals?
No prior experience is required. Neo4j Graph Database Fundamentals on CoddyKit is structured for beginners through advanced learners; this is — lesson 1 of 4, so you can start here or from the beginning and move at your own pace.
How long does the “Pathfinding Algorithms (BFS, DFS)” lesson take?
Most CoddyKit lessons take about 5–10 minutes. Each one is bite-sized and interactive, so you make steady progress and pick up exactly where you left off across the web and the app.
Can I write and run code in this Neo4j Graph Database Fundamentals lesson?
Yes. Every Neo4j Graph Database Fundamentals lesson includes a built-in code editor, so you write and run real code right in your browser and get instant AI feedback — no local setup required.
All lessons in this course
- Pathfinding Algorithms (BFS, DFS)
- Centrality Algorithms (PageRank)
- Community Detection Algorithms
- Similarity and Link Prediction Algorithms