265 research outputs found
Multi-scale Modularity in Complex Networks
We focus on the detection of communities in multi-scale networks, namely
networks made of different levels of organization and in which modules exist at
different scales. It is first shown that methods based on modularity are not
appropriate to uncover modules in empirical networks, mainly because modularity
optimization has an intrinsic bias towards partitions having a characteristic
number of modules which might not be compatible with the modular organization
of the system. We argue for the use of more flexible quality functions
incorporating a resolution parameter that allows us to reveal the natural
scales of the system. Different types of multi-resolution quality functions are
described and unified by looking at the partitioning problem from a dynamical
viewpoint. Finally, significant values of the resolution parameter are selected
by using complementary measures of robustness of the uncovered partitions. The
methods are illustrated on a benchmark and an empirical network.Comment: 8 pages, 3 figure
Temporal Pattern of Online Communication Spike Trains in Spreading a Scientific Rumor: How Often, Who Interacts with Whom?
We study complex time series (spike trains) of online user communication
while spreading messages about the discovery of the Higgs boson in Twitter. We
focus on online social interactions among users such as retweet, mention, and
reply, and construct different types of active (performing an action) and
passive (receiving an action) spike trains for each user. The spike trains are
analyzed by means of local variation, to quantify the temporal behavior of
active and passive users, as a function of their activity and popularity. We
show that the active spike trains are bursty, independently of their activation
frequency. For passive spike trains, in contrast, the local variation of
popular users presents uncorrelated (Poisson random) dynamics. We further
characterize the correlations of the local variation in different interactions.
We obtain high values of correlation, and thus consistent temporal behavior,
between retweets and mentions, but only for popular users, indicating that
creating online attention suggests an alignment in the dynamics of the two
interactions.Comment: A statistical data analysis & data mining on Social Dynamic Behavior,
9 pages and 7 figure
TiDeH: Time-Dependent Hawkes Process for Predicting Retweet Dynamics
Online social networking services allow their users to post content in the
form of text, images or videos. The main mechanism driving content diffusion is
the possibility for users to re-share the content posted by their social
connections, which may then cascade across the system. A fundamental problem
when studying information cascades is the possibility to develop sound
mathematical models, whose parameters can be calibrated on empirical data, in
order to predict the future course of a cascade after a window of observation.
In this paper, we focus on Twitter and, in particular, on the temporal patterns
of retweet activity for an original tweet. We model the system by
Time-Dependent Hawkes process (TiDeH), which properly takes into account the
circadian nature of the users and the aging of information. The input of the
prediction model are observed retweet times and structural information about
the underlying social network. We develop a procedure for parameter
optimization and for predicting the future profiles of retweet activity at
different time resolutions. We validate our methodology on a large corpus of
Twitter data and demonstrate its systematic improvement over existing
approaches in all the time regimes.Comment: The manuscript has been accepted in the 10th International AAAI
Conference on Web and Social Media (ICWSM 2016
Classes of random walks on temporal networks with competing timescales
Random walks find applications in many areas of science and are the heart of
essential network analytic tools. When defined on temporal networks, even basic
random walk models may exhibit a rich spectrum of behaviours, due to the
co-existence of different timescales in the system. Here, we introduce random
walks on general stochastic temporal networks allowing for lasting
interactions, with up to three competing timescales. We then compare the mean
resting time and stationary state of different models. We also discuss the
accuracy of the mathematical analysis depending on the random walk model and
the structure of the underlying network, and pay particular attention to the
emergence of non-Markovian behaviour, even when all dynamical entities are
governed by memoryless distributions.Comment: 16 pages, 5 figure
Preferential attachment with partial information
We propose a preferential attachment model for network growth where new
entering nodes have a partial information about the state of the network. Our
main result is that the presence of bounded information modifies the degree
distribution by introducing an exponential tail, while it preserves a power law
behaviour over a finite small range of degrees. On the other hand, unbounded
information is sufficient to let the network grow as in the standard
Barab\'asi-Albert model. Surprisingly, the latter feature holds true also when
the fraction of known nodes goes asymptotically to zero. Analytical results are
compared to direct simulations
Understanding Complex Systems: From Networks to Optimal Higher-Order Models
To better understand the structure and function of complex systems,
researchers often represent direct interactions between components in complex
systems with networks, assuming that indirect influence between distant
components can be modelled by paths. Such network models assume that actual
paths are memoryless. That is, the way a path continues as it passes through a
node does not depend on where it came from. Recent studies of data on actual
paths in complex systems question this assumption and instead indicate that
memory in paths does have considerable impact on central methods in network
science. A growing research community working with so-called higher-order
network models addresses this issue, seeking to take advantage of information
that conventional network representations disregard. Here we summarise the
progress in this area and outline remaining challenges calling for more
research.Comment: 8 pages, 4 figure
Coeovolutionary Threshold Dynamics
We present a generic threshold model for the co-evolution of the structure of
a network and the state of its nodes. We focus on regular directed networks and
derive equations for the evolution of the system toward its absorbing state. It
is shown that the system displays a transition from a connected phase to a
fragmented phase that depends on its initial configuration. Computer
simulations are performed and confirm the theoretical predictions.Comment: 4 pages, 4 figure
Imperfect spreading on temporal networks
We study spreading on networks where the contact dynamics between the nodes
is governed by a random process and where the inter-contact time distribution
may differ from the exponential. We consider a process of imperfect spreading,
where transmission is successful with a determined probability at each contact.
We first derive an expression for the inter-success time distribution,
determining the speed of the propagation, and then focus on a problem related
to epidemic spreading, by estimating the epidemic threshold in a system where
nodes remain infectious during a finite, random period of time. Finally, we
discuss the implications of our work to design an efficient strategy to enhance
spreading on temporal networks.Comment: 5 page
Dynamics of latent voters
We study the effect of latency on binary-choice opinion formation models.
Latency is introduced into the models as an additional dynamic rule: after a
voter changes its opinion, it enters a waiting period of stochastic length
where no further changes take place. We first focus on the voter model and show
that as a result of introducing latency, the average magnetization is not
conserved, and the system is driven toward zero magnetization, independently of
initial conditions. The model is studied analytically in the mean-field case
and by simulations in one dimension. We also address the behavior of the
Majority Rule model with added latency, and show that the competition between
imitation and latency leads to a rich phenomenology
Multiscale mixing patterns in networks
Assortative mixing in networks is the tendency for nodes with the same
attributes, or metadata, to link to each other. It is a property often found in
social networks manifesting as a higher tendency of links occurring between
people with the same age, race, or political belief. Quantifying the level of
assortativity or disassortativity (the preference of linking to nodes with
different attributes) can shed light on the factors involved in the formation
of links and contagion processes in complex networks. It is common practice to
measure the level of assortativity according to the assortativity coefficient,
or modularity in the case of discrete-valued metadata. This global value is the
average level of assortativity across the network and may not be a
representative statistic when mixing patterns are heterogeneous. For example, a
social network spanning the globe may exhibit local differences in mixing
patterns as a consequence of differences in cultural norms. Here, we introduce
an approach to localise this global measure so that we can describe the
assortativity, across multiple scales, at the node level. Consequently we are
able to capture and qualitatively evaluate the distribution of mixing patterns
in the network. We find that for many real-world networks the distribution of
assortativity is skewed, overdispersed and multimodal. Our method provides a
clearer lens through which we can more closely examine mixing patterns in
networks.Comment: 11 pages, 7 figure
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