This graph is a high level abstraction, of course. How exactly neurons store information is interesting, but hardly relevant here. My guess is that one symbol is stored in a very sparse subset of neurons and each neuron acts a bit like a node in a DHT. All together these neurons implement a fast DHT where a word2vec graph node acts as a key. On top of that this "wet DHT" can quickly find keys nearby, i.e. in can instantly return all neighbors of word2vec("apple").

I think ANNs implement only the word2vec function that translates images or sounds into symbols and vice versa.