graph
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graph
In mathematics and computer science, an abstract structure consisting of a set of objects (nodes) and the connections (edges) between them. It is used to represent networks and relationships.
Dijkstras Algorithmus findet den kürzesten Weg in einem Graphen.
Dijkstra's algorithm finds the shortest path in a graph.
'Graph' belongs to the word family around the Greek root '-graph-', which means 'to write' or 'to draw'. That is why it is also related to words like 'Grafik' (graphic) or 'grafisch' (graphic/graphical).
Eine gute Grafik kann komplexe Zusammenhänge einfach darstellen.
A good graphic can present complex relationships in a simple way.
Careful: while the English word 'graph' is often used generally for charts such as bar charts or pie charts, 'der Graph' (the graph) in German specifically refers to the mathematical representations mentioned here.
Der Graph der e-Funktion schneidet die y-Achse bei 1.
The graph of the exponential function intersects the y-axis at 1.
You can recognize the two meanings from the context. If people talk about 'Knoten' (nodes) and 'Kanten' (edges), they mean the structure from computer science. If it is about 'Funktionen' (functions) and 'Achsen' (axes), they mean the curve in a coordinate system.
Dieser Graph besteht aus fünf Knoten und sieben Kanten.
This graph consists of five nodes and seven edges.
In graph theory (mathematics, computer science), a graph always consists of 'Knoten' (nodes, or vertices) and 'Kanten' (edges), which connect the nodes to one another.
Soziale Netzwerke lassen sich als riesige Graphen darstellen.
Social networks can be represented as huge graphs.
In math class, 'Graph' almost always means the 'Graph einer Funktion' (graph of a function). This is drawn in a coordinate system with an x-axis and a y-axis.
Anhand des Graphen können wir sehen, wo die Funktion steigt und fällt.
Using the graph, we can see where the function rises and falls.
tree
'Baum' and 'Graph' can both describe a representation with points, lines, or branches, especially in mathematics, computer science, or diagrams. A 'Baum' usually shows a clear hierarchy: branches go downward or outward from a starting point, as in a family tree. A 'Graph' is more general: it can be a network of nodes and connections, or a curve in a coordinate system. Learners may confuse the words because a tree can look like a special kind of graph. In practical terms: for hierarchy and branching, 'Baum' fits; for networks or data curves, 'Graph' fits.
Der Graph zeigt, wie die Temperatur im Laufe des Tages gestiegen ist.
The graph shows how the temperature rose over the course of the day.
Im Kurs zeichnet die Lehrerin einen Baum, um die Familienbeziehungen zu zeigen.
In the course, the teacher draws a tree to show the family relationships.