Clone temporal centrality measures for incomplete sequences of graph snapshots

Different phenomena like the spread of a disease, social interactions or the biological relation between genes can be thought of as dynamic networks. These can be represented as a sequence of static graphs (so called graph snapshots). Based on this graph sequences, classical vertex centrality measures like closeness and betweenness centrality have been extended to quantify the importance of single vertices within a dynamic network. An implicit assumption for the calculation of temporal centrality measures is that the graph sequence contains all information about the network dynamics over time. This assumption is unlikely to be justified in many real world applications due to limited access to fully observed network data. Incompletely observed graph sequences lack important information about duration or existence of edges and may result in biased temporal centrality values.

To account for this incompleteness, we introduce the idea of extending original temporal centrality metrics by cloning graphs of an incomplete graph sequence. Focusing on temporal betweenness centrality as an example, we show for different simulated scenarios of incomplete graph sequences that our approach improves the accuracy of detecting important vertices in dynamic networks compared to the original methods. An age-related gene expression data set from the human brain illustrates the new measures. Additional results for the temporal closeness centrality based on cloned snapshots support our findings. We further introduce a new algorithm called REN to calculate temporal centrality measures. Its computational effort is linear in the number of snapshots and benefits from sparse or very dense dynamic networks.

We suggest to use clone temporal centrality measures in incomplete graph sequences settings. Compared to approaches that do not compensate for incompleteness our approach will improve the detection rate of important vertices. The proposed REN algorithm allows to calculate (clone) temporal centrality measures even for long snapshot sequences.