https://doi.org/10.1140/epjb/e2004-00111-4
Betweenness centrality in large complex networks
CEA, Département de Physique Théorique et Appliquée,
BP12 Bruyères-Le-Châtel, France
Corresponding author: a marc.barthelemy@cea.fr
Received:
18
September
2003
Revised:
11
December
2003
Published online:
14
May
2004
We analyze the betweenness centrality (BC) of nodes in large complex
networks. In general, the BC is increasing with connectivity as a
power law with an exponent η. We find that for trees or networks
with a small loop density 
while a larger density of loops
leads to 
. For scale-free networks characterized by an
exponent γ which describes the connectivity distribution decay,
the BC is also distributed according to a power law with a non
universal exponent δ. We show that this exponent δ must
satisfy the exact bound 
. If the scale free
network is a tree, then we have the equality 
.
PACS: 89.75.-k – Complex systems / 89.75.Hc – Networks and genealogical trees / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2004
