154,485 research outputs found
A survey of statistical network models
Networks are ubiquitous in science and have become a focal point for
discussion in everyday life. Formal statistical models for the analysis of
network data have emerged as a major topic of interest in diverse areas of
study, and most of these involve a form of graphical representation.
Probability models on graphs date back to 1959. Along with empirical studies in
social psychology and sociology from the 1960s, these early works generated an
active network community and a substantial literature in the 1970s. This effort
moved into the statistical literature in the late 1970s and 1980s, and the past
decade has seen a burgeoning network literature in statistical physics and
computer science. The growth of the World Wide Web and the emergence of online
networking communities such as Facebook, MySpace, and LinkedIn, and a host of
more specialized professional network communities has intensified interest in
the study of networks and network data. Our goal in this review is to provide
the reader with an entry point to this burgeoning literature. We begin with an
overview of the historical development of statistical network modeling and then
we introduce a number of examples that have been studied in the network
literature. Our subsequent discussion focuses on a number of prominent static
and dynamic network models and their interconnections. We emphasize formal
model descriptions, and pay special attention to the interpretation of
parameters and their estimation. We end with a description of some open
problems and challenges for machine learning and statistics.Comment: 96 pages, 14 figures, 333 reference
Generating realistic scaled complex networks
Research on generative models is a central project in the emerging field of
network science, and it studies how statistical patterns found in real networks
could be generated by formal rules. Output from these generative models is then
the basis for designing and evaluating computational methods on networks, and
for verification and simulation studies. During the last two decades, a variety
of models has been proposed with an ultimate goal of achieving comprehensive
realism for the generated networks. In this study, we (a) introduce a new
generator, termed ReCoN; (b) explore how ReCoN and some existing models can be
fitted to an original network to produce a structurally similar replica, (c)
use ReCoN to produce networks much larger than the original exemplar, and
finally (d) discuss open problems and promising research directions. In a
comparative experimental study, we find that ReCoN is often superior to many
other state-of-the-art network generation methods. We argue that ReCoN is a
scalable and effective tool for modeling a given network while preserving
important properties at both micro- and macroscopic scales, and for scaling the
exemplar data by orders of magnitude in size.Comment: 26 pages, 13 figures, extended version, a preliminary version of the
paper was presented at the 5th International Workshop on Complex Networks and
their Application
The Impact of Network Flows on Community Formation in Models of Opinion Dynamics
We study dynamics of opinion formation in a network of coupled agents. As the
network evolves to a steady state, opinions of agents within the same community
converge faster than those of other agents. This framework allows us to study
how network topology and network flow, which mediates the transfer of opinions
between agents, both affect the formation of communities. In traditional models
of opinion dynamics, agents are coupled via conservative flows, which result in
one-to-one opinion transfer. However, social interactions are often
non-conservative, resulting in one-to-many transfer of opinions. We study
opinion formation in networks using one-to-one and one-to-many interactions and
show that they lead to different community structure within the same network.Comment: accepted for publication in The Journal of Mathematical Sociology.
arXiv admin note: text overlap with arXiv:1201.238
Different approaches to community detection
A precise definition of what constitutes a community in networks has remained
elusive. Consequently, network scientists have compared community detection
algorithms on benchmark networks with a particular form of community structure
and classified them based on the mathematical techniques they employ. However,
this comparison can be misleading because apparent similarities in their
mathematical machinery can disguise different reasons for why we would want to
employ community detection in the first place. Here we provide a focused review
of these different motivations that underpin community detection. This
problem-driven classification is useful in applied network science, where it is
important to select an appropriate algorithm for the given purpose. Moreover,
highlighting the different approaches to community detection also delineates
the many lines of research and points out open directions and avenues for
future research.Comment: 14 pages, 2 figures. Written as a chapter for forthcoming Advances in
network clustering and blockmodeling, and based on an extended version of The
many facets of community detection in complex networks, Appl. Netw. Sci. 2: 4
(2017) by the same author
Mesoscopic structure conditions the emergence of cooperation on social networks
We study the evolutionary Prisoner's Dilemma on two social networks obtained
from actual relational data. We find very different cooperation levels on each
of them that can not be easily understood in terms of global statistical
properties of both networks. We claim that the result can be understood at the
mesoscopic scale, by studying the community structure of the networks. We
explain the dependence of the cooperation level on the temptation parameter in
terms of the internal structure of the communities and their interconnections.
We then test our results on community-structured, specifically designed
artificial networks, finding perfect agreement with the observations in the
real networks. Our results support the conclusion that studies of evolutionary
games on model networks and their interpretation in terms of global properties
may not be sufficient to study specific, real social systems. In addition, the
community perspective may be helpful to interpret the origin and behavior of
existing networks as well as to design structures that show resilient
cooperative behavior.Comment: Largely improved version, includes an artificial network model that
fully confirms the explanation of the results in terms of inter- and
intra-community structur
Temporal networks of face-to-face human interactions
The ever increasing adoption of mobile technologies and ubiquitous services
allows to sense human behavior at unprecedented levels of details and scale.
Wearable sensors are opening up a new window on human mobility and proximity at
the finest resolution of face-to-face proximity. As a consequence, empirical
data describing social and behavioral networks are acquiring a longitudinal
dimension that brings forth new challenges for analysis and modeling. Here we
review recent work on the representation and analysis of temporal networks of
face-to-face human proximity, based on large-scale datasets collected in the
context of the SocioPatterns collaboration. We show that the raw behavioral
data can be studied at various levels of coarse-graining, which turn out to be
complementary to one another, with each level exposing different features of
the underlying system. We briefly review a generative model of temporal contact
networks that reproduces some statistical observables. Then, we shift our focus
from surface statistical features to dynamical processes on empirical temporal
networks. We discuss how simple dynamical processes can be used as probes to
expose important features of the interaction patterns, such as burstiness and
causal constraints. We show that simulating dynamical processes on empirical
temporal networks can unveil differences between datasets that would otherwise
look statistically similar. Moreover, we argue that, due to the temporal
heterogeneity of human dynamics, in order to investigate the temporal
properties of spreading processes it may be necessary to abandon the notion of
wall-clock time in favour of an intrinsic notion of time for each individual
node, defined in terms of its activity level. We conclude highlighting several
open research questions raised by the nature of the data at hand.Comment: Chapter of the book "Temporal Networks", Springer, 2013. Series:
Understanding Complex Systems. Holme, Petter; Saram\"aki, Jari (Eds.
Low-temperature behaviour of social and economic networks
Real-world social and economic networks typically display a number of
particular topological properties, such as a giant connected component, a broad
degree distribution, the small-world property and the presence of communities
of densely interconnected nodes. Several models, including ensembles of
networks also known in social science as Exponential Random Graphs, have been
proposed with the aim of reproducing each of these properties in isolation.
Here we define a generalized ensemble of graphs by introducing the concept of
graph temperature, controlling the degree of topological optimization of a
network. We consider the temperature-dependent version of both existing and
novel models and show that all the aforementioned topological properties can be
simultaneously understood as the natural outcomes of an optimized,
low-temperature topology. We also show that seemingly different graph models,
as well as techniques used to extract information from real networks, are all
found to be particular low-temperature cases of the same generalized formalism.
One such technique allows us to extend our approach to real weighted networks.
Our results suggest that a low graph temperature might be an ubiquitous
property of real socio-economic networks, placing conditions on the diffusion
of information across these systems
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