Generalizing unweighted network measures to capture the focus in interactions

Unweighted network measures are commonly used to analyze real-world networks due to their simplicity and intuitiveness. This motivated the search for generalizations of unweighted network measures that take weights into account. We propose a new generalization methodology that captures how focused are the interactions over edges. The less focused the interaction (more uniform over edges) the closer is our generalization to the original unweighted measure. None of the previously developed generalizations capture this aspect of weighted networks. We analyze several real-world networks using our generalizations of the degree and the clustering coefficient. The analysis shows that our generalizations reveal interesting observations.