This participle is not used much in Swedish. I assume it is based on the verb "förgrena sig" (which has a reflexive or median sense, i.e. "to branch" in the intransitive sense).

Normally, the adjective "finförgrenad" would have been used, and I am assuming here that this is actually what the author intended.

Possibly, the author wanted to indicate a more active role for the net, as if it is "branching itself out", and thus chose this participle, in which case the English translation would be "finely branching" (which sounds as unusual in English as "finförgrenande" does in Swedish).