Temporal information plays a central role in shaping the structure of a network. In this paper, we consider the impact of an object on network structure over time. More specifically, we use a novel object-based dynamic measure to reflect the extent to which an object that is represented in the network by a vertex affects the topology of the network over time. By way of multigraph and Forman–Ricci flow, we assess the object’s impact on graph weights by comparing two graphs, one in which the object is present and one in which the object is absent. After using a case study to demonstrate the impact of Forman–Ricci flow on the network structure, we apply our measure in a semantic network to assess the effects of a word on the interactions between other words that follow it. In addition, we compare our novel measure to centrality and curvature measures so that we can ascertain the advantages of our measure over ones that already exist.
Bibliographical noteFunding Information:
This research was partially supported by the German-Israeli Foundation [grant I-1514-304.6/2019 to Emil Saucan and Jürgen Jost] and the Israel Science Foundation [grant 1471/20 to Anat Maril].
© 2022 by the authors.
- Forman–Ricci curvature
- Ricci flow
- complex network
- semantic network