Complex networks are virtually ubiquitous, and the Barabási and Albert model (BABA model) has became an acknowledged standard for the modelling of these systems. The so-called BABA model is a kind of preferential attachment growth model based on the intuitive premise that popularity is attractive. However, preferential attachment alone is insufficient to describe the diversity of complex networks observed in the real world. In this paper we first use the accuracy of a link prediction method, as a metric for network fitness. The link prediction method predicts the occurrence of links consistent with preferential attachment, the performance of this link prediction scheme is then a natural measure of the ”preferential-attachment-likeness” of a given network. We then propose several modification methods and modified BABA models to construct networks which more accurately describe the fitness properties of real networks. We find that all features assortativity, degree distribution and rich-club formation can play significant roles for the network construction and eventual structure. Moreover, link sparsity and the size of a network are key factors for network reconstruction. In addition, we find that the structure of the network which is limited by geographic location (nodes are embedded in a Euclidean space and connectivity is correlated with distances) differs from other typical networks. In social networks, we observe that the high school contact network has similar structure as the friends network and so we speculate that the contact behaviours can reflect real friendships.