What do you understand by graphs and trees? You might have listened to these terms other than in coding, but they play an essential role in the technical rounds of FAANG companies. So these two topics are a must-do for the interviews.
The main similarity between graphs and trees is that they both represent relationships between nodes. However, a key difference is that trees are a special type of graph with a hierarchical structure and no cycles, while graphs can have cycles and arbitrary connections.
Key Differences Between Graph and Tree
A tree is a hierarchical structure with nodes connected by edges and no cycles, while a graph is a broader structure that can have cycles and more complex connections between nodes. Trees are a subset of graphs.
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What is a Graph?
A graphis a non-linear data structure used to represent the networks, and it consists of vertices(V), or it can be called nodes and edges(E) that connect the pair of nodes.
In the graph, the edge can be directed or bidirected.
It can be weighted.
There are two commonly used representations of a graph are:
1. Adjacency Matrix
2. Adjacency List
Graphs are abstract mathematical structures composed of nodes (also called vertices) and edges (also called links or arcs) that connect these nodes. They are widely used to model various real-world systems and relationships, including social networks, transportation networks, computer networks, and more.
One of the key features of graphs is their versatility in representing diverse types of relationships. They can be directed or undirected, depending on whether the edges have a specific direction associated with them. Additionally, graphs can be weighted, meaning that each edge is assigned a numerical value to represent some attribute like distance, cost, or capacity.
Graphs also come in different forms, including sparse graphs with relatively few edges and dense graphs with many edges. Algorithms for traversing, searching, and analyzing graphs play a crucial role in computer science, with applications ranging from pathfinding in maps to recommendation systems in e-commerce.
There are two types of graphs:
Directed Graph:
A directed graph (or digraph) consists of nodes connected by edges, where each edge has a direction. This means that the relationship between nodes is one-way. For instance, if there is a directed edge from node A to node B, you can move from A to B but not necessarily from B to A. Directed graphs are useful for representing systems where relationships or flows are not reciprocal, such as one-way streets, workflows, or the structure of the internet (with hyperlinks as directed edges).
Directed Graph Characteristics
Each edge has a specific direction, indicating a one-way relationship between two nodes.
Often represented with arrows showing the direction of the relationship.
Useful in scenarios like workflows, dependencies, or web structures where relationships are one-way.
Nodes in a directed graph have an outdegree (edges leaving the node) and indegree (edges entering the node).
Can contain cycles, where you can follow edges in a directed loop back to the same node.
Undirected Graph:
In an undirected graph, edges do not have a direction. This means the relationship between nodes is bidirectional, and you can move freely between connected nodes in either direction. For example, if there is an edge between node A and node B, you can travel from A to B and also from B to A. Undirected graphs are ideal for representing mutual relationships like social networks, where friendships or connections are two-way.
Undirected Graph Characteristics
Edges in an undirected graph represent two-way, mutual relationships between nodes.
Typically shown with simple lines between nodes, with no direction implied.
Used in situations where connections are reciprocal, like social networks or undirected road networks.
Each node has a single degree, representing the total number of connections, regardless of direction.
Undirected graphs can also contain cycles, allowing you to traverse the nodes in a closed loop.
What is Tree?
The tree is a non-linear data structurethat offers relationships between the nodes in a structure and consists of nodes and edges, which arranges data items in sorted order and cannot be in the form of a cycle and should always be connected, unlike graphs.
There are several types of trees, such as a binary tree, binary search tree, AVL tree, threaded binary tree, B-tree, etc.
The topmost node is the tree's root, and all other nodes connected to it are its children(sub-nodes).
It does not contain any loop.
Trees are hierarchical data structures composed of nodes connected by edges that represent parent-child relationships. Unlike general graphs, trees have a single root node from which all other nodes descend, forming a branching structure without cycles.
One of the key characteristics of trees is their organization into levels, where each level corresponds to nodes at the same distance from the root. This hierarchical arrangement facilitates efficient data storage and retrieval, making trees useful in various applications such as organizing file systems, representing hierarchical data in databases, and implementing search algorithms like binary search trees.
Trees can take different forms, such as binary trees, where each node has at most two children, or balanced trees like AVL trees and red-black trees, which maintain balance to ensure efficient operations. Recursive algorithms are commonly used to traverse and manipulate tree structures, offering efficient solutions for tasks like sorting, searching, and indexing data.
What is the difference between tree search and graph search?
Tree search involves exploring hierarchical structures with a single root, employing algorithms like depth-first or breadth-first search. Graph search, on the other hand, navigates arbitrary connections, accounting for cycles and diverse node relationships, with algorithms such as Dijkstra's or A*.
What makes a graph a tree?
A graph becomes a tree when it forms a hierarchical structure without cycles, featuring a single root node from which all other nodes descend. Trees exhibit parent-child relationships, organized into levels, facilitating efficient storage and traversal operations in various applications.
Is every graph a tree?
No, not every graph is a tree. A tree is a specific type of graph with no cycles, but graphs can have cycles or disconnected nodes.
Which graph is called a tree?
A graph is called a tree if it is connected, has no cycles, and contains exactly n−1n-1n−1 edges for nnn nodes.
Which graph is not a tree?
A graph with cycles or disconnected components is not a tree. Any graph with more or fewer than n−1n-1n−1 edges for nnn nodes isn't a tree.
Can a tree have zero edges?
Yes, a tree can have zero edges, but this only occurs when there is a single node, which is considered a trivial tree.
Conclusion
In this blog, we have covered the two non-linear data structures and how they differ in their properties.
Graphs and trees are used to solve various complex problems in competitive programming. The graph is a Data Structure where vertices are connected using edges and form a cycle. Whereas Trees is a data structure where the topmost node is the tree's root, and all others are its children, it cannot have a cycle.
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