Recently developed concepts and techniques of analyzing complex
systems provide new insight into the structure of social networks.
Uncovering recurrent preferences and organizational principles in such
networks is a key issue to characterize them. We investigate school
friendship networks from the Add Health database. Applying threshold
analysis, we find that the friendship networks do not form a single
connected component through mutual strong nominations within a school,
while under weaker conditions such interconnectedness is present. We
extract the networks of overlapping communities at the schools
(c-networks) and find that they are scale free and disassortative in
contrast to the direct friendship networks, which have an exponential
degree distribution and are assortative. Based on the network analysis
we study the ethnic preferences in friendship selection. The clique
percolation method we use reveals that when in minority, the students
tend to build more densely interconnected groups of friends. We also
find an asymmetry in the behavior of black minorities in a white
majority as compared to that of white minorities in a black majority.
We study the size distribution of power blackouts for the Norwegian
and North American power grids. We find that for both systems the size
distribution follows power laws with exponents -1.65±0.05 and
-2.0±0.1 respectively. We then present a model with global
redistribution of the load when a link in the system fails which
reproduces the power law from the Norwegian power grid if the
simulation are carried out on the Norwegian high-voltage power grid.
The model is also applied to regular and irregular networks and give
power laws with exponents -2.0±0.05 for the regular networks and
-1.5±0.05 for the irregular networks. A presented mean field
theory is in good agreement with these numerical results.
Electronic databases, from phone to emails logs, currently provide
detailed records of human communication patterns, offering novel
avenues to map and explore the structure of social and communication
networks. Here we examine the communication patterns of millions of
mobile phone users, allowing us to simultaneously study the local and
the global structure of a society-wide communication network. We
observe a coupling between interaction strengths and the network's
local structure, with the counterintuitive consequence that social
networks are robust to the removal of the strong ties, but fall apart
following a phase transition if the weak ties are removed. We show
that this coupling significantly slows the diffusion process,
resulting in dynamic trapping of information in communities, and find
that when it comes to information diffusion, weak and strong ties are
both simultaneously ineffective.
We consider a system hierarchically modular, if besides its hierarchical structure it shows a sequence of scale separations from the point of view of some functionality or property. Starting from regular, deterministic objects like the Vicsek snowflake or the deterministic scale free network by Ravasz et al. we first characterize the hierarchical modularity by the periodicity of some properties on a logarithmic scale indicating separation of scales. Then we introduce randomness by keeping the scale freeness and other important characteristics of the objects and monitor the changes in the modularity. In the presented examples sufficient amount of randomness destroys hierarchical modularity. Our findings suggest that the experimentally observed hierarchical modularity in systems with algebraically decaying clustering coefficients indicates a limited level of randomness.