Comparison of influence measures on structural changes focused on node functions

Abstract

The structures of some real-world networks are dynamic in nature as time goes by. These changes consist of the addition or deletion of nodes or links and the rewiring of links. Even if link rewiring occurs, the influence degree tends to differ depending on the location in which it occurs, the nature of the nodes, and so forth. In this paper, by quantifying the influence degree of each node, we attempt to extract the influential structural changes wherein each node in a large population changes its function. Concretely, we define the node function as the PageRank convergence curve of the node and the influence degree affecting the node as distance based on a correlation coefficient of convergence curves before and after change occurs. We then propose the Structural Change Influence Measure (SCIM), which is the average value of the influence degree of all nodes. Based on experimental evaluation using several synthetic and real networks, we found five promising properties of our proposed measure. Our method indicates a higher value for changes in: 1) number of link rewirings; 2) concentrated link deleting; 3) link addition between distant nodes; 4) link addition between important and unimportant nodes; and 5) link deletion between communities.