Graph vs. Tree — What's the Difference?

A mathematical structure representing nodes connected by edges.

A graph often used to represent decision-making processes.

A diagram showing data relationships visually.

A hierarchical graph with a root node and branching connections.

A structure allowing for loops and multiple connections.

A graph with no cycles, ensuring a single path from root to nodes.

A structure without a hierarchical root system.

A directed acyclic graph representing hierarchical relationships.

A structure that can be directed or undirected.

A data structure widely used in computer science.

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.

In botany, a tree is a perennial plant with an elongated stem, or trunk, supporting branches and leaves in most species. In some usages, the definition of a tree may be narrower, including only wood plants with secondary growth, plants that are usable as lumber or plants above a specified height.

A pictorial device, such as a pie chart or bar graph, used to illustrate quantitative relationships. Also called chart.

A woody perennial plant, typically having a single stem or trunk growing to a considerable height and bearing lateral branches at some distance from the ground.

The spelling of a word.

A wooden structure or part of a structure.

Any of the possible forms of a grapheme.

A thing that has a branching structure resembling that of a tree.

A written character that represents a vowel, consonant, syllable, word, or other expression and that cannot be further analyzed.

Force (a hunted animal) to take refuge in a tree.

To represent by a graph.

(of an area) planted with trees

To plot (a function) on a graph.

A perennial woody plant having a main trunk and usually a distinct crown.

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.

An herbaceous plant or shrub resembling a tree in form or size.

(mathematics) A set of points constituting a graphical representation of a real function; (formally) a set of tuples $(x\_1,\; x\_2,\; \backslash ldots,\; x\_m,\; y)\backslash in\backslash R^\{m+1\}$, where $y=f(x\_1,\; x\_2,\; \backslash ldots,\; x\_m)$ for a given function $f:\; \backslash R^m\backslash rightarrow\backslash R$. See also Graph of a function Category:en:Curves Category:en:Functions

Something that resembles a tree in form, especially a diagram or arrangement that has branches showing relationships of hierarchy or lineage.

(graph theory) A set of vertices (or nodes) connected together by edges; (formally) an ordered pair of sets $(V,E)$, where the elements of $V$ are called vertices or nodes and $E$ is a set of pairs (called edges) of elements of $V$. See also Graph (discrete mathematics)

(Computers) A structure for organizing or classifying data in which every item can be traced to a single origin through a unique path.

(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.

A wooden beam, post, stake, or bar used as part of a framework or structure.

A morphism $\backslash Gamma\_f$ from the domain of $f$ to the product of the domain and codomain of $f$, such that the first projection applied to $\backslash Gamma\_f$ equals the identity of the domain, and the second projection applied to $\backslash Gamma\_f$ is equal to $f$.

A saddletree.

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.

A gallows.

(transitive) To draw a graph.

The cross on which Jesus was crucified.

To draw a graph of a function.

To force up a tree

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.

(Informal) To force into a difficult position; corner

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.

To supply or cover with trees

A drawing illustrating the relations between certain quantities plotted with reference to a set of axes

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.

Represent by means of a graph;

Any plant that is reminiscent of the above but not classified as a tree (in any botanical sense).

Plot upon a graph

An object made from a tree trunk and having multiple hooks or storage platforms.

A device used to hold or stretch a shoe open.

The structural frame of a saddle.

(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.

(computing theory) A recursive data structure in which each node has zero or more nodes as children.

(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.

Any structure or construct having branches representing divergence or possible choices.

The structure or wooden frame used in the construction of a saddle used in horse riding.

Marijuana.

(obsolete) A cross or gallows.

(chemistry) A mass of crystals, aggregated in arborescent forms, obtained by precipitation of a metal from solution.

(cartomancy) The fifth Lenormand card.

(transitive) To chase (an animal or person) up a tree.

(transitive) To place in a tree.

(transitive) To place upon a tree; to fit with a tree; to stretch upon a tree.

(intransitive) To take refuge in a tree.

Any perennial woody plant of considerable size (usually over twenty feet high) and growing with a single trunk.

Something constructed in the form of, or considered as resembling, a tree, consisting of a stem, or stock, and branches; as, a genealogical tree.

A piece of timber, or something commonly made of timber; - used in composition, as in axletree, boottree, chesstree, crosstree, whiffletree, and the like.

A cross or gallows; as Tyburn tree.

Wood; timber.

A mass of crystals, aggregated in arborescent forms, obtained by precipitation of a metal from solution. See Lead tree, under Lead.

To drive to a tree; to cause to ascend a tree; as, a dog trees a squirrel.

A tall perennial woody plant having a main trunk and branches forming a distinct elevated crown; includes both gymnosperms and angiosperms

A figure that branches from a single root;

English actor and theatrical producer noted for his lavish productions of Shakespeare (1853-1917)

Chase a bear up a tree with dogs and kill it

Yes, a tree is a special kind of graph without cycles and with a hierarchical structure.

Not necessarily; graphs can be disconnected, meaning there might not be paths between all nodes.

No, a tree has a singular root node, unlike graphs which don't have a root.

Yes, trees are directed graphs, with all edges pointing away from the root node.

Common types include binary trees, binary search trees, AVL trees, and red-black trees, each with specific properties and uses.

Graphs are used to model relationships between entities, useful in various fields like social networking, transportation networks, and computer science.

Yes, graphs can have weighted edges, where each edge has a value representing the strength or capacity of the connection.

A graph allows arbitrary connections and cycles, while a tree has strict hierarchical rules with no cycles.

A rooted tree has a designated root node that defines a hierarchical structure, whereas a free tree doesn't have a fixed root and can be viewed as undirected.

In general trees, there are no specific limits. However, in binary trees, each node can have no more than two children.

A graph is cyclic if it has at least one cycle, a path where the first and last nodes are the same. An acyclic graph has no such cycles.

In directed graphs, edges have a direction indicating a one-way relationship, whereas undirected graphs have edges that represent two-way relationships.

Trees can be traversed in various ways including in-order, pre-order, and post-order, each visiting nodes in a different sequence.

A spanning tree is a subset of a graph that includes all the vertices connected by the minimum number of edges needed to maintain connectivity without any cycles.

The depth of a tree is the number of edges on the longest path from the root node to the furthest leaf node.