Graph vs. Tree: Know the Difference
By Shumaila Saeed || Updated on December 26, 2023
A graph is a collection of nodes connected by edges with no specific structure, while a tree is a hierarchical structure of nodes, where each node has only one parent except the root node.
Key Differences
A graph is a set of nodes connected by edges, not necessarily following a hierarchical structure. A tree is a special form of a graph where nodes are arranged hierarchically, with a single root node and sub-nodes.
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Dec 26, 2023
In a graph, edges can connect any two nodes, and cycles are possible. In a tree, each node (except the root) is connected to exactly one parent node, and cycles are not allowed.
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Dec 26, 2023
Graphs can be more complex and flexible in structure, allowing for various types of connections. Trees have a more rigid structure, with a clear parent-child relationship among nodes.
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Graphs are used in scenarios like social networks, where connections are diverse. Trees are used in scenarios like file systems, where a hierarchical organization is needed.
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Graphs come in various types, such as directed, undirected, weighted, and unweighted. Trees also have types like binary trees, AVL trees, and B-trees, each with specific properties.
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Dec 26, 2023
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Comparison Chart
XStructure
Can have any arrangement of nodes and edges
Hierarchical structure with a single root
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Edge Connections
Edges can connect any nodes, allowing cycles
Edges connect nodes in a parent-child relationship, no cycles
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Node Relationship
Nodes have no defined parent-child relationship
Every node (except root) has exactly one parent
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Common Uses
Network modeling, path finding
Organizational charts, data storage
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Graph and Tree Definitions
Graph
A diagram showing the relation between variable quantities.
The graph plotted temperature against time.
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Tree
A hierarchical model with a single root and branches.
The tree structure was used to organize the database.
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Graph
A mathematical structure used to model pairwise relations.
The graph illustrated the social network connections.
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Tree
A connected graph with no cycles.
The tree showed a clear lineage of the royal family.
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Graph
A network of nodes that may or may not form a cycle.
The graph depicted various routes between airports.
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Tree
A structure with nodes representing parent-child relationships.
The organizational chart was designed as a tree.
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Graph
A diagram that exhibits a relationship, often functional, between two sets of numbers as a set of points having coordinates determined by the relationship. Also called plot.
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Tree
A perennial woody plant having a main trunk and usually a distinct crown.
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Graph
A pictorial device, such as a pie chart or bar graph, used to illustrate quantitative relationships. Also called chart.
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Oct 19, 2023
Tree
Something that resembles a tree in form, especially a diagram or arrangement that has branches showing relationships of hierarchy or lineage.
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Tree
(Computers) A structure for organizing or classifying data in which every item can be traced to a single origin through a unique path.
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Graph
A written character that represents a vowel, consonant, syllable, word, or other expression and that cannot be further analyzed.
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Tree
A wooden beam, post, stake, or bar used as part of a framework or structure.
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Graph
A data chart (graphical representation of data) intended to illustrate the relationship between a set (or sets) of numbers (quantities, measurements or indicative numbers) and a reference set, whose elements are indexed to those of the former set(s) and may or may not be numbers.
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Graph
(mathematics) A set of points constituting a graphical representation of a real function; (formally) a set of tuples , where for a given function . See also Graph of a function Category:en:Curves Category:en:Functions
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Graph
(graph theory) A set of vertices (or nodes) connected together by edges; (formally) an ordered pair of sets , where the elements of are called vertices or nodes and is a set of pairs (called edges) of elements of . See also Graph (discrete mathematics)
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Tree
(Informal) To force into a difficult position; corner
The reporters finally treed the mayor.
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Graph
(topology) A topological space which represents some graph (ordered pair of sets) and which is constructed by representing the vertices as points and the edges as copies of the real interval [0,1] (where, for any given edge, 0 and 1 are identified with the points representing the two vertices) and equipping the result with a particular topology called the graph topology.
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Graph
A morphism from the domain of to the product of the domain and codomain of , such that the first projection applied to equals the identity of the domain, and the second projection applied to is equal to .
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Tree
A perennial woody plant, not exactly defined, but differentiated from a shrub by its larger size (typically over a few meters in height) or growth habit, usually having a single (or few) main axis or trunk unbranched for some distance above the ground and a head of branches and foliage.
Hyperion is the tallest living tree in the world.
Birds have a nest in a tree in the garden.
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Graph
A graphical unit on the token-level, the abstracted fundamental shape of a character or letter as distinct from its ductus (realization in a particular typeface or handwriting on the instance-level) and as distinct by a grapheme on the type-level by not fundamentally distinguishing meaning.
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Tree
Any plant that is reminiscent of the above but not classified as a tree (in any botanical sense).
The banana tree
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Tree
An object made from a tree trunk and having multiple hooks or storage platforms.
He had the choice of buying a scratching post or a cat tree.
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Graph
A curve or surface, the locus of a point whose coördinates are the variables in the equation of the locus; as, a graph of the exponential function.
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Graph
A diagram symbolizing a system of interrelations of variable quantities using points represented by spots, or by lines to represent the relations of continuous variables. More than one set of interrelations may be presented on one graph, in which case the spots or lines are typically distinguishable from each other, as by color, shape, thickness, continuity, etc. A diagram in which relationships between variables are represented by other visual means is sometimes called a graph, as in a bar graph, but may also be called a chart.
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Tree
(graph theory) A connected graph with no cycles or, if the graph is finite, equivalently a connected graph with n vertices and n−1 edges.
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Graph
A drawing illustrating the relations between certain quantities plotted with reference to a set of axes
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Tree
(computing theory) A recursive data structure in which each node has zero or more nodes as children.
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Tree
(graphical user interface) A display or listing of entries or elements such that there are primary and secondary entries shown, usually linked by drawn lines or by indenting to the right.
We’ll show it as a tree list.
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Tree
Any structure or construct having branches representing divergence or possible choices.
Family tree; skill tree
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Graph
A collection of points (vertices) connected by lines (edges).
In this graph, each vertex represents a city.
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Tree
The structure or wooden frame used in the construction of a saddle used in horse riding.
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Graph
A visual representation of data to show trends.
The bar graph displayed the company's sales data.
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Tree
(chemistry) A mass of crystals, aggregated in arborescent forms, obtained by precipitation of a metal from solution.
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Tree
(transitive) To chase (an animal or person) up a tree.
The dog treed the cat.
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Tree
(transitive) To place in a tree.
Black bears can tree their cubs for protection, but grizzly bears cannot.
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Tree
(transitive) To place upon a tree; to fit with a tree; to stretch upon a tree.
To tree a boot
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Tree
Any perennial woody plant of considerable size (usually over twenty feet high) and growing with a single trunk.
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Tree
Something constructed in the form of, or considered as resembling, a tree, consisting of a stem, or stock, and branches; as, a genealogical tree.
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Tree
A piece of timber, or something commonly made of timber; - used in composition, as in axletree, boottree, chesstree, crosstree, whiffletree, and the like.
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Tree
A cross or gallows; as Tyburn tree.
[Jesus] whom they slew and hanged on a tree.
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Tree
Wood; timber.
In a great house ben not only vessels of gold and of silver but also of tree and of earth.
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Tree
A mass of crystals, aggregated in arborescent forms, obtained by precipitation of a metal from solution. See Lead tree, under Lead.
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Tree
To drive to a tree; to cause to ascend a tree; as, a dog trees a squirrel.
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Tree
A tall perennial woody plant having a main trunk and branches forming a distinct elevated crown; includes both gymnosperms and angiosperms
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Tree
English actor and theatrical producer noted for his lavish productions of Shakespeare (1853-1917)
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Tree
A data structure used in computer science.
Binary trees are commonly used in search algorithms.
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Tree
A model used to depict hierarchical information.
The tree diagram helped in decision-making processes.
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Repeatedly Asked Queries
What defines a tree?
A tree is a hierarchical structure of nodes with one parent per node.
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Dec 26, 2023
What are some types of graphs?
Types include directed, undirected, weighted, and unweighted graphs.
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How are graphs used in computer science?
Graphs model networks, relationships, and pathfinding problems.
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What is a binary tree?
A binary tree is a tree where each node has up to two children.
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How is a directed graph different?
In a directed graph, edges have a direction, indicating a one-way relationship.
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What are examples of tree structures?
Examples include binary trees, AVL trees, and B-trees.
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Can graphs represent real-world networks?
Yes, graphs are ideal for modeling real-world networks.
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Is a tree always binary?
No, trees can have various numbers of children per node.
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What is the root of a tree?
The root is the topmost node in a tree, without a parent.
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What is the significance of edges in a graph?
Edges represent connections between nodes in a graph.
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What makes a tree hierarchical?
Its structure of one parent per node, except for the root.
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Can a tree have disconnected branches?
No, all nodes in a tree are connected by a path to the root.
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Do graphs need to have connected components?
No, graphs can have disconnected components.
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Are graph algorithms applicable to trees?
Yes, many graph algorithms can be applied to trees as well.
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Dec 26, 2023
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About Author
Written by
Shumaila SaeedShumaila Saeed, an expert content creator with 6 years of experience, specializes in distilling complex topics into easily digestible comparisons, shining a light on the nuances that both inform and educate readers with clarity and accuracy.
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