||Complex network provide a new platform to study of complex system where many interesting properties can be related to the topological properties of the network. Recent examples can be found in the scale free distribution for nodes in Internet and the Small World in the social network. However, correlation with neighbours are not yet fully mathematical analysis of the nearest neighbour correlation, which is described well by the Aboav-Weaire law in two dimensional cellular structure and apply the analysis for various artificial as well as real network. The Aboav-Weaire law is a semi-empirical law which can relate the evolution of network with entropy change in the system The Aboav-Weaire Law in Complex network provides a new tool for classification of network and new insights into complex network. The second part of the thesis is the application of complex network analysis to predict protein structure. By analysis the protein sequence, we map it into a complex network and apply the mathematical tools such as degree distribution and correlation to discuss various protein sequence and collocation pairs are also investigated in details, both analytically and numerically. We found an extensive relation between constructed complex network and its real folded structure. For example: the characteristics path length of collocation pair network shows high similarity with the real pairwise distance and can be used a predictor for the folded structure. Furthermore, we found that all collocation pair network show consistence with the Aboav-Weaire law with the Aboav parameter different from different protein structures. An interpretation of theses correlations in the context of the biochemistry can be made. Other features such as the clustering coefficient and mean degree found in complex network can also be explain and related to the Biological property of protein.