127 research outputs found
Complex Contagions in Kleinberg's Small World Model
Complex contagions describe diffusion of behaviors in a social network in
settings where spreading requires the influence by two or more neighbors. In a
-complex contagion, a cluster of nodes are initially infected, and
additional nodes become infected in the next round if they have at least
already infected neighbors. It has been argued that complex contagions better
model behavioral changes such as adoption of new beliefs, fashion trends or
expensive technology innovations. This has motivated rigorous understanding of
spreading of complex contagions in social networks. Despite simple contagions
() that spread fast in all small world graphs, how complex contagions
spread is much less understood. Previous work~\cite{Ghasemiesfeh:2013:CCW}
analyzes complex contagions in Kleinberg's small world
model~\cite{kleinberg00small} where edges are randomly added according to a
spatial distribution (with exponent ) on top of a two dimensional grid
structure. It has been shown in~\cite{Ghasemiesfeh:2013:CCW} that the speed of
complex contagions differs exponentially when compared to when
.
In this paper, we fully characterize the entire parameter space of
except at one point, and provide upper and lower bounds for the speed of
-complex contagions. We study two subtly different variants of Kleinberg's
small world model and show that, with respect to complex contagions, they
behave differently. For each model and each , we show that there is
an intermediate range of values, such that when takes any of these
values, a -complex contagion spreads quickly on the corresponding graph, in
a polylogarithmic number of rounds. However, if is outside this range,
then a -complex contagion requires a polynomial number of rounds to spread
to the entire network.Comment: arXiv admin note: text overlap with arXiv:1404.266
Long ties accelerate noisy threshold-based contagions
Network structure can affect when and how widely new ideas, products, and
behaviors are adopted. In widely-used models of biological contagion,
interventions that randomly rewire edges (generally making them "longer")
accelerate spread. However, there are other models relevant to social
contagion, such as those motivated by myopic best-response in games with
strategic complements, in which an individual's behavior is described by a
threshold number of adopting neighbors above which adoption occurs (i.e.,
complex contagions). Recent work has argued that highly clustered, rather than
random, networks facilitate spread of these complex contagions. Here we show
that minor modifications to this model, which make it more realistic, reverse
this result: we allow very rare below-threshold adoption, i.e., rarely adoption
occurs when there is only one adopting neighbor. To model the trade-off between
long and short edges we consider networks that are the union of cycle-power-
graphs and random graphs on nodes. Allowing adoptions below threshold to
occur with order probability along some "short" cycle edges is
enough to ensure that random rewiring accelerates spread. Simulations
illustrate the robustness of these results to other commonly-posited models for
noisy best-response behavior. Hypothetical interventions that randomly rewire
existing edges or add random edges (versus adding "short", triad-closing edges)
in hundreds of empirical social networks reduce time to spread. This revised
conclusion suggests that those wanting to increase spread should induce
formation of long ties, rather than triad-closing ties. More generally, this
highlights the importance of noise in game-theoretic analyses of behavior
Disconnected, fragmented, or united? A trans-disciplinary review of network science
During decades the study of networks has been divided between the efforts of
social scientists and natural scientists, two groups of scholars who often do
not see eye to eye. In this review I present an effort to mutually translate
the work conducted by scholars from both of these academic fronts hoping to
continue to unify what has become a diverging body of literature. I argue that
social and natural scientists fail to see eye to eye because they have
diverging academic goals. Social scientists focus on explaining how context
specific social and economic mechanisms drive the structure of networks and on
how networks shape social and economic outcomes. By contrast, natural
scientists focus primarily on modeling network characteristics that are
independent of context, since their focus is to identify universal
characteristics of systems instead of context specific mechanisms. In the
following pages I discuss the differences between both of these literatures by
summarizing the parallel theories advanced to explain link formation and the
applications used by scholars in each field to justify their approach to
network science. I conclude by providing an outlook on how these literatures
can be further unified
Recommended from our members
A Multiplex Social Contagion Dynamics Model to Shape and Discriminate D2D Content Dissemination
- …