  The identification of nodes occupying important positions in a network
structure is crucial for the understanding of the associated real-world system.
Usually, betweenness centrality is used to evaluate a node capacity to connect
different graph regions. However, we argue here that this measure is not
adapted for that task, as it gives equal weight to "local" centers (i.e. nodes
of high degree central to a single region) and to "global" bridges, which
connect different communities. This distinction is important as the roles of
such nodes are different in terms of the local and global organisation of the
network structure. In this paper we propose a decomposition of betweenness
centrality into two terms, one highlighting the local contributions and the
other the global ones. We call the latter bridgeness centrality and show that
it is capable to specifically spot out global bridges. In addition, we
introduce an effective algorithmic implementation of this measure and
demonstrate its capability to identify global bridges in air transportation and
scientific collaboration networks.
