Detection of network inhomogeneity by total neighbor degree

Inhomogeneity in networks can be detected by the analysis of the correlation of the total degree of nearest neighbors. This is illustrated by two models. The first one is a random multi-partitions network that the Aboav Weaire law, which predicts the linear relationship between the degree of node and the total degree of nearest neighbor, is being extended. The second one is a preferential attachment network with two partitions which shows scale free properties with power tail $\gamma$ within the range $2<\gamma\le3$. By plotting the total degree of neighbor verses the degree of each node in the networks, the scattered plot shows separable clustering as evidence for inhomogeneity in networks. The effectiveness of this new tool for the detection of inhomogeneity is demonstrated in real bipartite networks. By using this method, some interesting group of nodes of semantic and WWW networks have been found.