Absolute Expressiveness of Subgraph Motif Centrality Measures

In graph-based applications, a common task is to pinpoint the most important or ``central'' vertex in a (directed or undirected) graph, or rank the vertices of a graph according to their importance. To this end, a plethora of so-called centrality measures have been proposed in the literature that assess which vertices in a graph are the most important ones. Riveros and Salas, in an ICDT 2020 paper, proposed a family of centrality measures based on the following intuitive principle: the importance of a vertex in a graph is relative to the number of ``relevant'' connected subgraphs, known as subgraph motifs, surrounding it. We refer to the measures derived from the above principle as subgraph motif measures. It has been convincingly argued that subgraph motif measures are well-suited for graph database applications. Although the ICDT paper studied several favourable properties enjoyed by subgraph motif measures, their absolute expressiveness remains largely unexplored. The goal of this work is to precisely characterize the absolute expressiveness of the family of subgraph motif measures.