73,622 research outputs found
The Evolution of Beliefs over Signed Social Networks
We study the evolution of opinions (or beliefs) over a social network modeled
as a signed graph. The sign attached to an edge in this graph characterizes
whether the corresponding individuals or end nodes are friends (positive links)
or enemies (negative links). Pairs of nodes are randomly selected to interact
over time, and when two nodes interact, each of them updates its opinion based
on the opinion of the other node and the sign of the corresponding link. This
model generalizes DeGroot model to account for negative links: when two enemies
interact, their opinions go in opposite directions. We provide conditions for
convergence and divergence in expectation, in mean-square, and in almost sure
sense, and exhibit phase transition phenomena for these notions of convergence
depending on the parameters of the opinion update model and on the structure of
the underlying graph. We establish a {\it no-survivor} theorem, stating that
the difference in opinions of any two nodes diverges whenever opinions in the
network diverge as a whole. We also prove a {\it live-or-die} lemma, indicating
that almost surely, the opinions either converge to an agreement or diverge.
Finally, we extend our analysis to cases where opinions have hard lower and
upper limits. In these cases, we study when and how opinions may become
asymptotically clustered to the belief boundaries, and highlight the crucial
influence of (strong or weak) structural balance of the underlying network on
this clustering phenomenon
Absorbing Random Walks Interpolating Between Centrality Measures on Complex Networks
Centrality, which quantifies the "importance" of individual nodes, is among
the most essential concepts in modern network theory. As there are many ways in
which a node can be important, many different centrality measures are in use.
Here, we concentrate on versions of the common betweenness and it closeness
centralities. The former measures the fraction of paths between pairs of nodes
that go through a given node, while the latter measures an average inverse
distance between a particular node and all other nodes. Both centralities only
consider shortest paths (i.e., geodesics) between pairs of nodes. Here we
develop a method, based on absorbing Markov chains, that enables us to
continuously interpolate both of these centrality measures away from the
geodesic limit and toward a limit where no restriction is placed on the length
of the paths the walkers can explore. At this second limit, the interpolated
betweenness and closeness centralities reduce, respectively, to the well-known
it current betweenness and resistance closeness (information) centralities. The
method is tested numerically on four real networks, revealing complex changes
in node centrality rankings with respect to the value of the interpolation
parameter. Non-monotonic betweenness behaviors are found to characterize nodes
that lie close to inter-community boundaries in the studied networks
A Relational Hyperlink Analysis of an Online Social Movement
In this paper we propose relational hyperlink analysis (RHA) as a distinct approach for empirical social science research into hyperlink networks on the World Wide Web. We demonstrate this approach, which employs the ideas and techniques of social network analysis (in particular, exponential random graph modeling), in a study of the hyperlinking behaviors of Australian asylum advocacy groups. We show that compared with the commonly-used hyperlink counts regression approach, relational hyperlink analysis can lead to fundamentally different conclusions about the social processes underpinning hyperlinking behavior. In particular, in trying to understand why social ties are formed, counts regressions may over-estimate the role of actor attributes in the formation of hyperlinks when endogenous, purely structural network effects are not taken into account. Our analysis involves an innovative joint use of two software programs: VOSON, for the automated retrieval and processing of considerable quantities of hyperlink data, and LPNet, for the statistical modeling of social network data. Together, VOSON and LPNet enable new and unique research into social networks in the online world, and our paper highlights the importance of complementary research tools for social science research into the web
Missing data in multiplex networks: a preliminary study
A basic problem in the analysis of social networks is missing data. When a
network model does not accurately capture all the actors or relationships in
the social system under study, measures computed on the network and ultimately
the final outcomes of the analysis can be severely distorted. For this reason,
researchers in social network analysis have characterised the impact of
different types of missing data on existing network measures. Recently a lot of
attention has been devoted to the study of multiple-network systems, e.g.,
multiplex networks. In these systems missing data has an even more significant
impact on the outcomes of the analyses. However, to the best of our knowledge,
no study has focused on this problem yet. This work is a first step in the
direction of understanding the impact of missing data in multiple networks. We
first discuss the main reasons for missingness in these systems, then we
explore the relation between various types of missing information and their
effect on network properties. We provide initial experimental evidence based on
both real and synthetic data.Comment: 7 page
Modeling spatial social complex networks for dynamical processes
The study of social networks --- where people are located, geographically,
and how they might be connected to one another --- is a current hot topic of
interest, because of its immediate relevance to important applications, from
devising efficient immunization techniques for the arrest of epidemics, to the
design of better transportation and city planning paradigms, to the
understanding of how rumors and opinions spread and take shape over time. We
develop a spatial social complex network (SSCN) model that captures not only
essential connectivity features of real-life social networks, including a
heavy-tailed degree distribution and high clustering, but also the spatial
location of individuals, reproducing Zipf's law for the distribution of city
populations as well as other observed hallmarks. We then simulate Milgram's
Small-World experiment on our SSCN model, obtaining good qualitative agreement
with the known results and shedding light on the role played by various network
attributes and the strategies used by the players in the game. This
demonstrates the potential of the SSCN model for the simulation and study of
the many social processes mentioned above, where both connectivity and
geography play a role in the dynamics.Comment: 10 pages, 6 figure
Parallel Algorithms for Generating Random Networks with Given Degree Sequences
Random networks are widely used for modeling and analyzing complex processes.
Many mathematical models have been proposed to capture diverse real-world
networks. One of the most important aspects of these models is degree
distribution. Chung--Lu (CL) model is a random network model, which can produce
networks with any given arbitrary degree distribution. The complex systems we
deal with nowadays are growing larger and more diverse than ever. Generating
random networks with any given degree distribution consisting of billions of
nodes and edges or more has become a necessity, which requires efficient and
parallel algorithms. We present an MPI-based distributed memory parallel
algorithm for generating massive random networks using CL model, which takes
time with high probability and space per processor,
where , , and are the number of nodes, edges and processors,
respectively. The time efficiency is achieved by using a novel load-balancing
algorithm. Our algorithms scale very well to a large number of processors and
can generate massive power--law networks with one billion nodes and
billion edges in one minute using processors.Comment: Accepted in NPC 201
Uncovering nodes that spread information between communities in social networks
From many datasets gathered in online social networks, well defined community
structures have been observed. A large number of users participate in these
networks and the size of the resulting graphs poses computational challenges.
There is a particular demand in identifying the nodes responsible for
information flow between communities; for example, in temporal Twitter networks
edges between communities play a key role in propagating spikes of activity
when the connectivity between communities is sparse and few edges exist between
different clusters of nodes. The new algorithm proposed here is aimed at
revealing these key connections by measuring a node's vicinity to nodes of
another community. We look at the nodes which have edges in more than one
community and the locality of nodes around them which influence the information
received and broadcasted to them. The method relies on independent random walks
of a chosen fixed number of steps, originating from nodes with edges in more
than one community. For the large networks that we have in mind, existing
measures such as betweenness centrality are difficult to compute, even with
recent methods that approximate the large number of operations required. We
therefore design an algorithm that scales up to the demand of current big data
requirements and has the ability to harness parallel processing capabilities.
The new algorithm is illustrated on synthetic data, where results can be judged
carefully, and also on a real, large scale Twitter activity data, where new
insights can be gained
Sizing the length of complex networks
Among all characteristics exhibited by natural and man-made networks the
small-world phenomenon is surely the most relevant and popular. But despite its
significance, a reliable and comparable quantification of the question `how
small is a small-world network and how does it compare to others' has remained
a difficult challenge to answer. Here we establish a new synoptic
representation that allows for a complete and accurate interpretation of the
pathlength (and efficiency) of complex networks. We frame every network
individually, based on how its length deviates from the shortest and the
longest values it could possibly take. For that, we first had to uncover the
upper and the lower limits for the pathlength and efficiency, which indeed
depend on the specific number of nodes and links. These limits are given by
families of singular configurations that we name as ultra-short and ultra-long
networks. The representation here introduced frees network comparison from the
need to rely on the choice of reference graph models (e.g., random graphs and
ring lattices), a common practice that is prone to yield biased interpretations
as we show. Application to empirical examples of three categories (neural,
social and transportation) evidences that, while most real networks display a
pathlength comparable to that of random graphs, when contrasted against the
absolute boundaries, only the cortical connectomes prove to be ultra-short
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