How come the neuter noun 'δίκτυο' is linked with an adjective 'δημοφιλές' which does not appear to be neuter? Or is this an odd declension?
Most adjectives in Greek have three kinds of endings: masculine, feminine, and neuter.
For example, "good" can be καλός, καλή, καλό in the singular and καλοί, καλές, καλά in the plural.
But there are some adjectives that have just two kinds of endings: one for masculine and feminine and another one for neuter.
For example, ο δημοφιλής, η δημοφιλής, το δημοφιλές (popular) or ο ευγνώμων, η ευγνώμων, το ευγνώμον (thankful, grateful).
These are often originally compound words - in this example from δήμος + φιλία or ευ + γνώμη.
This also explains why έγκυος seems to have a masculine ending even when it applies to women -- it's also a compound word (the first part is εν "in" but I don't know what the second part is - it doesn't exist as a separate word any more as far as I know) and so it's a two-ending adjective with the masculine and feminine endings being the same.