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. Such measures assess
which vertices in a graph are the most important ones by analyzing the
structure of the underlying graph. A family of centrality measures that are
suited for graph databases has been recently proposed by relying on the
following simple principle: the importance of a vertex in a graph is relative
to the number of ``relevant'' connected subgraphs surrounding it; we refer to
the members of this family as subgraph-based centrality measures. Although it
has been shown that such measures enjoy several favourable properties, their
absolute expressiveness remains largely unexplored. The goal of this work is to
precisely characterize the absolute expressiveness of the family of
subgraph-based centrality measures by considering both directed and undirected
graphs. To this end, we characterize when an arbitrary centrality measure is a
subgraph-based one, or a subgraph-based measure relative to the induced
ranking. These characterizations provide us with technical tools that allow us
to determine whether well-established centrality measures are subgraph-based.
Such a classification, apart from being interesting in its own right, gives
useful insights on the structural similarities and differences among existing
centrality measures.

本文研究了基于子图的中心性测量方法在有向图和无向图中的表现，并提供了技术工具来确定现有中心性测量方法是否属于基于子图的测量方法。