das Geflecht
weave
A structure created by weaving or intertwining threads, branches, or similar material.
Der Korb besteht aus einem feinen Geflecht aus Weidenruten.
The basket consists of a fine weave of willow rods.

weave / network
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weave
A structure created by weaving or intertwining threads, branches, or similar material.
Der Korb besteht aus einem feinen Geflecht aus Weidenruten.
The basket consists of a fine weave of willow rods.

'Das Geflecht' (the weave/network) is derived from the verb 'flechten' (to make something by intertwining material). The prefix 'Ge-' here often indicates the result of an action.
Ihre Haare waren zu einem kunstvollen Zopf geflochten.
Her hair was braided into an elaborate plait.
In its concrete meaning, 'Geflecht' (weave) is often combined with the material it consists of. Typical formulations are 'ein Geflecht aus' + material or 'ein Geflecht von' + material.
Der Stuhl hat eine Sitzfläche aus einem Geflecht von Rattan.
The chair has a seat made of a weave of rattan.
You can recognize the figurative meaning by the fact that 'Geflecht' (network) is combined with abstract nouns such as 'Beziehungen' (relationships), 'Lügen' (lies), 'Interessen' (interests), or 'Korruption' (corruption).
Es war schwierig, das komplexe Geflecht aus persönlichen und beruflichen Beziehungen zu verstehen.
It was difficult to understand the complex network of personal and professional relationships.
system
'das System' and 'das Geflecht' can both mean a whole made up of many connected parts. 'System' emphasizes order, function, and clear connections. You can explain how it works. 'Geflecht' emphasizes that many things are closely interwoven, for example relationships, interests, or rules. It often sounds less clear and orderly than 'System'. The words can be confused when something is complex. If the structure is ordered and functional, 'System' fits. If the connections are dense, hard to separate, and complicated, 'Geflecht' is more precise.

In der Firma gibt es ein dichtes Geflecht aus alten Kontakten und Interessen.
In the company, there is a dense network of old contacts and interests.
Für die Prüfung lernst du zuerst das System der deutschen Fälle.
For the exam, you first learn the system of German cases.