  We construct a connected network of 3.9 million nodes from mobile phone call
records, which can be regarded as a proxy for the underlying human
communication network at the societal level. We assign two weights on each edge
to reflect the strength of social interaction, which are the aggregate call
duration and the cumulative number of calls placed between the individuals over
a period of 18 weeks. We present a detailed analysis of this weighted network
by examining its degree, strength, and weight distributions, as well as its
topological assortativity and weighted assortativity, clustering and weighted
clustering, together with correlations between these quantities. We give an
account of motif intensity and coherence distributions and compare them to a
randomized reference system. We also use the concept of link overlap to measure
the number of common neighbors any two adjacent nodes have, which serves as a
useful local measure for identifying the interconnectedness of communities. We
report a positive correlation between the overlap and weight of a link, thus
providing strong quantitative evidence for the weak ties hypothesis, a central
concept in social network analysis. The percolation properties of the network
are found to depend on the type and order of removed links, and they can help
understand how the local structure of the network manifests itself at the
global level. We hope that our results will contribute to modeling weighted
large-scale social networks, and believe that the systematic approach followed
here can be adopted to study other weighted networks.
