||The study of complex networks provides us with a brand new perspective to understand nature and also reveals that nature is far from being random. Our work focuses on the topological analysis of networks in terms of nearest neighbor degree correlation. It is described by the semi-empirical Aboav- Weaire Law which has been verified in various real and artificial systems. In this thesis, we generalize this law from the nearest to long distance neighbors degree correlation in different artificial network models as well as real systems. We also report two practical applications of the Aboav- Weaire law in identifying two special classes of networks, the hierarchical network and the bipartite network. In the study of the bipartite metabolic network of 43 different organisms, we have found a data collapse in the Aboav curves which shows that these networks have high level of structural similarity. We also borrowed the concept of topological charge from two-dimensional cellular network and defined an analogy of the Aboav- Weaire Law for directed networks. We have tested our tools in co-occurrence language network, protein interaction network, World Wide Web network, AS level Internet network and food webs. We have discovered a universal behavior in the average neighboring charge in these networks and it is different from the Aboav- Weaire Law in undirected networks.