306 research outputs found
Analysis of weighted networks
The connections in many networks are not merely binary entities, either
present or not, but have associated weights that record their strengths
relative to one another. Recent studies of networks have, by and large, steered
clear of such weighted networks, which are often perceived as being harder to
analyze than their unweighted counterparts. Here we point out that weighted
networks can in many cases be analyzed using a simple mapping from a weighted
network to an unweighted multigraph, allowing us to apply standard techniques
for unweighted graphs to weighted ones as well. We give a number of examples of
the method, including an algorithm for detecting community structure in
weighted networks and a new and simple proof of the max-flow/min-cut theorem.Comment: 9 pages, 3 figure
Universality in movie rating distributions
In this paper histograms of user ratings for movies (1,...,10) are analysed.
The evolving stabilised shapes of histograms follow the rule that all are
either double- or triple-peaked. Moreover, at most one peak can be on the
central bins 2,...,9 and the distribution in these bins looks smooth
`Gaussian-like' while changes at the extremes (1 and 10) often look abrupt. It
is shown that this is well approximated under the assumption that histograms
are confined and discretised probability density functions of L\'evy skew
alpha-stable distributions. These distributions are the only stable
distributions which could emerge due to a generalized central limit theorem
from averaging of various independent random avriables as which one can see the
initial opinions of users. Averaging is also an appropriate assumption about
the social process which underlies the process of continuous opinion formation.
Surprisingly, not the normal distribution achieves the best fit over histograms
obseved on the web, but distributions with fat tails which decay as power-laws
with exponent -(1+alpha) (alpha=4/3). The scale and skewness parameters of the
Levy skew alpha-stable distributions seem to depend on the deviation from an
average movie (with mean about 7.6). The histogram of such an average movie has
no skewness and is the most narrow one. If a movie deviates from average the
distribution gets broader and skew. The skewness pronounces the deviation. This
is used to construct a one parameter fit which gives some evidence of
universality in processes of continuous opinion dynamics about taste.Comment: 8 pages, 5 figures, accepted for publicatio
Generalized Master Equations for Non-Poisson Dynamics on Networks
The traditional way of studying temporal networks is to aggregate the
dynamics of the edges to create a static weighted network. This implicitly
assumes that the edges are governed by Poisson processes, which is not
typically the case in empirical temporal networks. Consequently, we examine the
effects of non-Poisson inter-event statistics on the dynamics of edges, and we
apply the concept of a generalized master equation to the study of
continuous-time random walks on networks. We show that the equation reduces to
the standard rate equations when the underlying process is Poisson and that the
stationary solution is determined by an effective transition matrix whose
leading eigenvector is easy to calculate. We discuss the implications of our
work for dynamical processes on temporal networks and for the construction of
network diagnostics that take into account their nontrivial stochastic nature
Collective Decision Dynamics in the Presence of External Drivers
We develop a sequence of models describing information transmission and
decision dynamics for a network of individual agents subject to multiple
sources of influence. Our general framework is set in the context of an
impending natural disaster, where individuals, represented by nodes on the
network, must decide whether or not to evacuate. Sources of influence include a
one-to-many externally driven global broadcast as well as pairwise
interactions, across links in the network, in which agents transmit either
continuous opinions or binary actions. We consider both uniform and variable
threshold rules on the individual opinion as baseline models for
decision-making. Our results indicate that 1) social networks lead to
clustering and cohesive action among individuals, 2) binary information
introduces high temporal variability and stagnation, and 3) information
transmission over the network can either facilitate or hinder action adoption,
depending on the influence of the global broadcast relative to the social
network. Our framework highlights the essential role of local interactions
between agents in predicting collective behavior of the population as a whole.Comment: 14 pages, 7 figure
Cascades on clique-based graphs
peer-reviewedWe present an analytical approach to determining the expected cascade size in a broad range of dynamical models on the class of highly clustered random graphs introduced by Gleeson [J. P. Gleeson, Phys. Rev. E 80, 036107 (2009)]. A condition for the existence of global cascades is also derived. Applications of this approach include analyses of percolation, and Watts's model. We show how our techniques can be used to study the effects of in-group bias in cascades on social networks.PUBLISHEDpeer-reviewe
Local Convergence and Global Diversity: From Interpersonal to Social Influence
Axelrod (1997) showed how local convergence in cultural influence can
preserve cultural diversity. We argue that central implications of Axelrod's
model may change profoundly, if his model is integrated with the assumption of
social influence as assumed by an earlier generation of modelers. Axelrod and
all follow up studies employed instead the assumption that influence is
interpersonal (dyadic). We show how the combination of social influence with
homophily allows solving two important problems. Our integration of social
influence yields monoculture in small societies and diversity increasing in
population size, consistently with empirical evidence but contrary to earlier
models. The second problem was identified by Klemm et al.(2003a,b), an
extremely narrow window of noise levels in which diversity with local
convergence can be obtained at all. Our model with social influence generates
stable diversity with local convergence across a much broader interval of noise
levels than models based on interpersonal influence.Comment: 20 pages, 3 figures, Paper presented at American Sociological
Association 103rd Annual Meeting, August 1-4, 2008, Boston, MA. Session on
Mathematical Sociolog
Correlation between centrality metrics and their application to the opinion model
In recent decades, a number of centrality metrics describing network
properties of nodes have been proposed to rank the importance of nodes. In
order to understand the correlations between centrality metrics and to
approximate a high-complexity centrality metric by a strongly correlated
low-complexity metric, we first study the correlation between centrality
metrics in terms of their Pearson correlation coefficient and their similarity
in ranking of nodes. In addition to considering the widely used centrality
metrics, we introduce a new centrality measure, the degree mass. The m order
degree mass of a node is the sum of the weighted degree of the node and its
neighbors no further than m hops away. We find that the B_{n}, the closeness,
and the components of x_{1} are strongly correlated with the degree, the
1st-order degree mass and the 2nd-order degree mass, respectively, in both
network models and real-world networks. We then theoretically prove that the
Pearson correlation coefficient between x_{1} and the 2nd-order degree mass is
larger than that between x_{1} and a lower order degree mass. Finally, we
investigate the effect of the inflexible antagonists selected based on
different centrality metrics in helping one opinion to compete with another in
the inflexible antagonists opinion model. Interestingly, we find that selecting
the inflexible antagonists based on the leverage, the B_{n}, or the degree is
more effective in opinion-competition than using other centrality metrics in
all types of networks. This observation is supported by our previous
observations, i.e., that there is a strong linear correlation between the
degree and the B_{n}, as well as a high centrality similarity between the
leverage and the degree.Comment: 20 page
Academic team formation as evolving hypergraphs
This paper quantitatively explores the social and socio-semantic patterns of
constitution of academic collaboration teams. To this end, we broadly underline
two critical features of social networks of knowledge-based collaboration:
first, they essentially consist of group-level interactions which call for
team-centered approaches. Formally, this induces the use of hypergraphs and
n-adic interactions, rather than traditional dyadic frameworks of interaction
such as graphs, binding only pairs of agents. Second, we advocate the joint
consideration of structural and semantic features, as collaborations are
allegedly constrained by both of them. Considering these provisions, we propose
a framework which principally enables us to empirically test a series of
hypotheses related to academic team formation patterns. In particular, we
exhibit and characterize the influence of an implicit group structure driving
recurrent team formation processes. On the whole, innovative production does
not appear to be correlated with more original teams, while a polarization
appears between groups composed of experts only or non-experts only, altogether
corresponding to collectives with a high rate of repeated interactions
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A Multilevel Measurement Model of Social Cohesion
In spite of its currency both in academic research and political rhetoric, there are numerous attempts to define and conceptualize the social cohesion concept but there has been paid little attention to provide a rigorous and empirically tested definition. There are even fewer studies that address social cohesion in a framework of cross-cultural validation of the indicators testing the equivalence of the factorial structure across countries. Finally, as far as we know there is no study that attempt to provide an empirically tested multilevel definition of social cohesion specifying a Multilevel Structural Equation Model. This study aims to cover this gap. First, we provide a theoretical construct of social cohesion taking into account not only its multidimensionality but also its multilevel structure. In the second step, to test the validity of this theoretical construct, we perform a multilevel confirmatory factor analysis in order to verify if the conceptual structure suggested in first step holds. In addition, we test the cross-level structural equivalence and the measurement invariance of the model in order to verify if the same multilevel model of social cohesion holds across the 29 countries analysed. In the final step, we specify a second-order multilevel CFA model in order to identify the existence of a general factor that can be called “social cohesion” operating in society that accounts for the surface phenomena that we observe
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Validation of a social cohesion theoretical framework: a multiple group SEM strategy
Social cohesion dates back to the end of the nineteenth century. Back then, society experienced epochal transformations, as are also happening nowadays. Whenever there are epochal changes, a social order (cohesion) matter arises. The paper provides a conceptual scheme of social cohesion identifying its constituent dimensions subdivided by three spheres (macro, meso, micro) and two perspectives (objective and subjective). The overarching aim is to test the validity of the operationalization of the social cohesion model provided. Firstly, we conducted an exploratory factor analysis introducing an approach implemented in Mplus named exploratory structural equation modeling that shows several useful characteristics. Afterward, through a structural equation modeling approach, we performed several confirmatory factor analyses adopting a multiple group SEM strategy in order to cross-validate the social cohesion model
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