The structure of social networks influences dynamic processes of human interaction and communication, such
as opinion formation and spreading of information or infectious diseases. To facilitate simulation studies of
such processes, we have developed a weighted network model to resemble the structure of real social networks, in
particular taking into account recent observations on weight-topology correlations. The model iterates on a fixed
size network, reaching a steady state through processes of weighted local searches, global random attachment, and
random deletion of nodes. There are essentially two parameters which can be used to tune network properties.
The generated networks display community structure, with strong internal links and weak links connecting the
communities. Similarly to empirical observations, strong ties correlate with overlapping neighbourhoods, and
under edge removal, the network becomes fragmented faster when weak ties are removed first. As an example
of the effects that such structural properties have on dynamic processes, we present early results from studies of
social dynamics describing the competition of two non-excluding opinions in a society, showing that the weighted
community structure slows down the dynamics as compared to randomized references.
We review the decomposition method of stock return cross-correlations, presented previously for studying the
dependence of the correlation coefficient on the resolution of data (Epps effect). Through a toy model of random
walk/Brownian motion and memoryless renewal process (i.e. Poisson point process) of observation times we
show that in case of analytical treatability, by decomposing the correlations we get the exact result for the
frequency dependence. We also demonstrate that our approach produces reasonable fitting of the dependence
of correlations on the data resolution in case of empirical data. Our results indicate that the Epps phenomenon
is a product of the finite time decay of lagged correlations of high resolution data, which does not scale with
activity. The characteristic time is due to a human time scale, the time needed to react to news.
Financial markets can be described on several time scales. We use data from the limit order book of the
London Stock Exchange (LSE) to compare how the fluctuation dominated microstructure crosses over to a more
systematic global behavior.
Detecting community structure in real-world networks is a challenging problem. Recently, it has been shown
that the resolution of methods based on optimizing a modularity measure or a corresponding energy is limited;
communities with sizes below some threshold remain unresolved. One possibility to go around this problem is to
vary the threshold by using a tuning parameter, and investigate the community structure at variable resolutions.
Here, we analyze the resolution limit and multiresolution behavior for two different methods: a q-state Potts
method proposed by Reichard and Bornholdt, and a recent multiresolution method by Arenas, Fernandez, and
Gomez. These methods are studied analytically, and applied to three test networks using simulated annealing.
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