Difference Between Tree and Graph

Have you ever wondered about the key differences between trees and graphs in data structures? A tree is a hierarchical structure with a single root and no cycles, ensuring a unique path between any two nodes. In contrast, a graph is a more flexible representation, allowing for cycles, multiple paths between nodes, and potentially no single root, accommodating complex relationships like networks. Let's understand more!

A tree is a hierarchical data structure that consists of nodes connected by edges, and a graph is a more general data structure compared to a tree and is used to represent complex relationships between objects. In this blog, we will understand the differences between them in detail!

Table of Content

• Difference Between Tree and Graph
• What is a Tree?
• What is a Graph?
• Similarities Between Tree and Graph

Difference Between Tree and Graph

Below is a table differentiating between tree and graph.

What is a Tree?

A tree is a fundamental data structure used in computer science and information theory that simulates a hierarchical tree structure with a set of connected nodes. It is a special case of a graph; more specifically, it is an acyclic-connected graph where one node is designated as the root.

Components of Tree

• Node: The basic unit of a tree, representing an element or a data point in the tree. Each node can contain data and also may link to other nodes (its children).
• Root: The top node of the tree from which all other nodes descend. The root node is the only node in the tree that does not have a parent.
• Edge (Link): A connection between two nodes, representing the relationship (typically parent-child) between them. The edge directly connects one node to another in the tree structure.
• Parent: A node that has one or more child nodes. In a tree, every node (except the root) has exactly one parent, which is the node directly above it.
• Child: A node that is a descendant of another node. A node can have zero or more children. Nodes with the same parent are called siblings.
• Sibling: Nodes that share the same parent are siblings. They are on the same level of the tree.
• Leaf (Terminal Node): A node with no children. Leaves are the final nodes on branches; they do not contain any reference to other nodes.
• Subtree: A section of a tree consisting of a node and all its descendants. Each node in a tree can be viewed as the root of a subtree.
• Level: The level of a node is determined by its distance from the root. The root is at level 1, its children are at level 2, and so on.
• Depth (or Height) of a Node: The length of the path from the root to the node, measured by the number of edges in the path. The depth of the root is 0.
• Height of a Tree: The maximum depth among all the nodes in the tree. It is the length of the longest path from the root to a leaf.
• Degree of a Node: The number of children a node has. In binary trees, a node can have a degree of 0, 1, or 2.
• Path: A sequence of nodes and edges connecting a pair of nodes. Each pair of nodes in a tree has exactly one path connecting them.

What is a Graph?

A graph is a fundamental data structure in computer science and discrete mathematics that consists of a set of nodes (or vertices) and a set of edges that establish relationships between these nodes. Graphs are used to represent networks of connections and relationships between objects, making them invaluable for modeling a wide variety of systems in computer algorithms, network analysis, social network modeling, and more. 

Components of Graph

• Vertex (or Node): A vertex represents an entity or a data point within a graph. The collection of vertices in a graph is often denoted as V. Each vertex can have zero or more connections to other vertices in the graph.
• Edge: An edge is a connection between two vertices, representing the relationship or link between them. The collection of edges in a graph is often denoted as E. Edges can be either undirected (bidirectional) or directed (unidirectional), and they can connect a vertex to itself (a loop).
• Weight (Optional): In weighted graphs, each edge can have a weight or cost associated with it, representing the magnitude of the connection or relationship (e.g., distance, time, or capacity). Graphs without edge weights are considered unweighted.
• Path: A path in a graph is a sequence of vertices where each adjacent pair of vertices is connected by an edge. In directed graphs, the path follows the direction of the edges.
• Cycle: A cycle is a path that starts and ends at the same vertex, with all edges and vertices (except the starting/ending vertex) distinct. In directed graphs, these are referred to as directed cycles.
• Directed Graph (Digraph): A graph where the edges have a direction, indicating a one-way relationship from one vertex to another. The edges in a directed graph are often called arcs.
• Undirected Graph: A graph where the edges do not have a direction, indicating a two-way, bidirectional relationship between the vertices connected by each edge.
• Subgraph: A subgraph is a subset of a graph's vertices and edges that forms a graph itself. A subgraph can be induced by a subset of vertices (including all edges between those vertices) or by a subset of edges (including all vertices incident to those edges).
• Connected Graph: In an undirected graph, it is connected if there is a path between every pair of vertices. In a directed graph, connectivity can be more complex, with concepts such as strongly connected (a path exists in both directions between every pair of vertices) and weakly connected (replacing all directed edges with undirected edges results in a connected graph).
• Degree: The degree of a vertex is the number of edges incident to it. In directed graphs, this is further divided into in-degree (the number of incoming edges) and out-degree (the number of outgoing edges).
• Adjacency: Two vertices are considered adjacent if they are connected by an edge. In a similar vein, two edges are adjacent if they share a common vertex.
• Graph Order and Size: The order of a graph is the number of its vertices, and the size of a graph is the number of its edges.

Similarities Between Tree and Graph

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Thus, understanding these distinctions is crucial for choosing the appropriate data structure for a given problem, whether it's organizing data in a hierarchical manner using trees or modeling complex networks with potentially cyclical relationships using graphs. Each structure offers unique advantages and limitations. Keep learning, keep exploring!