A tree is a data structure built from nodes connected by edges, with exactly one path between any two nodes and no cycles, no way to start at a node and follow connections back to that same node again. A graph generalises this structure by dropping that no-cycles restriction entirely, allowing nodes to connect to each other in essentially any pattern, including cycles, multiple paths between the same two nodes, and connections that loop back on themselves. That one relaxed rule is exactly what lets graphs model considerably messier real-world relationships that a tree's stricter, more limited structure simply can't represent.
A tree's strict structure rules out a huge range of real relationships
A tree's requirement of exactly one path between any two nodes, with no cycles at all, works well for representing strictly hierarchical relationships, a company's organisational chart, a file system's folder structure, where each item has one clear, single parent. But this same strict requirement makes a tree structurally incapable of representing relationships that don't follow this clean hierarchy, a social network where two people can be connected through several genuinely different paths at once, or a road network where multiple distinct routes connect the same two cities.
Graphs represent these messier relationships by simply allowing more connections
A graph handles exactly these more complex cases by allowing nodes to connect to each other far more flexibly, with no restriction against multiple paths between the same two nodes or against cycles forming somewhere in the structure. Traversing a graph, visiting its nodes systematically, requires genuinely more careful algorithms than traversing a tree does, specifically because a graph's traversal has to actively track which nodes have already been visited to avoid getting caught in an infinite loop around a cycle, a concern that simply doesn't arise in a cycle-free tree. This added traversal complexity is precisely the trade-off graphs accept in exchange for their much greater structural flexibility.
What we're still unsure about
The basic distinction between trees and graphs, and the traversal algorithms needed to handle a graph's cycles correctly, are precisely defined, well established computer science, confirmed across an enormous range of practical applications. What's more genuinely an ongoing area of applied research is developing more efficient algorithms for analysing especially large, complex real-world graphs, social networks or web-scale link structures with billions of nodes and connections, since many otherwise well-understood graph algorithms become impractically slow at that kind of scale — computer scientists continue actively developing faster, more scalable approaches for exactly these largest, most complex graph structures, rather than every graph problem already having an equally efficient solution at any scale.
This sits inside Graphs (Representations & Traversal), one of eight topics in Data Structures, one of seven domains in Computer Science, one of seventeen subjects the app can quiz you on.