Bitcoins and Blockchain technologies are attracting the attention of different scientific communities. In addition, their widespread industrial applications and the continuous introduction of cryptocurrencies are also stimulating the attention of the public opinion. The underlying structure of these technologies constitutes one of their core concepts. In particular, they are based on peer-to-peer networks. Accordingly, all nodes lie at the same level, so that there is no place for privileged actors as, for instance, banking institutions in classical financial networks. In this work, we perform a preliminary investigation on two kinds of network, i.e. the Bitcoin network and the Bitcoin Cash network. Notably, we analyze their global structure and we try to evaluate if they are provided with a small-world behavior. Results suggest that the principle known as 'fittest-gets-richer', combined with a continuous increasing of connections, might constitute the mechanism leading these networks to reach their current structure. Moreover, further observations open the way to new investigations into this direction.