The most common and most likely answer to this crossword clue is the 4 letter word WIFI
I've seen this crossword clue in Financial Times
W
I
F
I
More clues leading to the result WIFI
Buddy explains!

The straight part
We know that "Network" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case network = wifi.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does WIFI mean?
WIFI noun- Any of several standards for short-range wireless data transmission (IEEE 802.11).
- Wireless networking using one of these standards.
- The capability to connect to a Wi-Fi network.