25,803 research outputs found
Threshold for the Outbreak of Cascading Failures in Degree-degree Uncorrelated Networks
In complex networks, the failure of one or very few nodes may cause cascading
failures. When this dynamical process stops in steady state, the size of the
giant component formed by remaining un-failed nodes can be used to measure the
severity of cascading failures, which is critically important for estimating
the robustness of networks. In this paper, we provide a cascade of overload
failure model with local load sharing mechanism, and then explore the threshold
of node capacity when the large-scale cascading failures happen and un-failed
nodes in steady state cannot connect to each other to form a large connected
sub-network. We get the theoretical derivation of this threshold in
degree-degree uncorrelated networks, and validate the effectiveness of this
method in simulation. This threshold provide us a guidance to improve the
network robustness under the premise of limited capacity resource when creating
a network and assigning load. Therefore, this threshold is useful and important
to analyze the robustness of networks.Comment: 11 pages, 4 figure
Impact of Community Structure on Cascades
The threshold model is widely used to study the propagation of opinions and
technologies in social networks. In this model, individuals adopt the new
behavior based on how many neighbors have already chosen it. Specifically, we
consider the permanent adoption model where individuals that have adopted the
new behavior cannot change their state. We study cascades under the threshold
model on sparse random graphs with community structure to see whether the
existence of communities affects the number of individuals who finally adopt
the new behavior.
When seeding a small number of agents with the new behavior, the community
structure has little effect on the final proportion of people that adopt it,
i.e., the contagion threshold is the same as if there were just one community.
On the other hand, seeding a fraction of the population with the new behavior
has a significant impact on the cascade with the optimal seeding strategy
depending on how strongly the communities are connected. In particular, when
the communities are strongly connected, seeding in one community outperforms
the symmetric seeding strategy that seeds equally in all communities. We also
investigate the problem of optimum seeding given a budget constraint, and
propose a gradient-based heuristic seeding strategy. Our algorithm,
numerically, dispels commonly held beliefs in the literature that suggest the
best seeding strategy is to seed over the nodes with the highest number of
neighbors.Comment: Version to be published to EC 201
Analysis of complex contagions in random multiplex networks
We study the diffusion of influence in random multiplex networks where links
can be of different types, and for a given content (e.g., rumor, product,
political view), each link type is associated with a content dependent
parameter in that measures the relative bias type- links
have in spreading this content. In this setting, we propose a linear threshold
model of contagion where nodes switch state if their "perceived" proportion of
active neighbors exceeds a threshold \tau. Namely, a node connected to
active neighbors and inactive neighbors via type- links will turn
active if exceeds its threshold \tau. Under this
model, we obtain the condition, probability and expected size of global
spreading events. Our results extend the existing work on complex contagions in
several directions by i) providing solutions for coupled random networks whose
vertices are neither identical nor disjoint, (ii) highlighting the effect of
content on the dynamics of complex contagions, and (iii) showing that
content-dependent propagation over a multiplex network leads to a subtle
relation between the giant vulnerable component of the graph and the global
cascade condition that is not seen in the existing models in the literature.Comment: Revised 06/08/12. 11 Pages, 3 figure
Modeling self-sustained activity cascades in socio-technical networks
The ability to understand and eventually predict the emergence of information
and activation cascades in social networks is core to complex socio-technical
systems research. However, the complexity of social interactions makes this a
challenging enterprise. Previous works on cascade models assume that the
emergence of this collective phenomenon is related to the activity observed in
the local neighborhood of individuals, but do not consider what determines the
willingness to spread information in a time-varying process. Here we present a
mechanistic model that accounts for the temporal evolution of the individual
state in a simplified setup. We model the activity of the individuals as a
complex network of interacting integrate-and-fire oscillators. The model
reproduces the statistical characteristics of the cascades in real systems, and
provides a framework to study time-evolution of cascades in a state-dependent
activity scenario.Comment: 5 pages, 3 figure
Virus Propagation in Multiple Profile Networks
Suppose we have a virus or one competing idea/product that propagates over a
multiple profile (e.g., social) network. Can we predict what proportion of the
network will actually get "infected" (e.g., spread the idea or buy the
competing product), when the nodes of the network appear to have different
sensitivity based on their profile? For example, if there are two profiles
and in a network and the nodes of profile
and profile are susceptible to a highly spreading
virus with probabilities and
respectively, what percentage of both profiles will actually get infected from
the virus at the end? To reverse the question, what are the necessary
conditions so that a predefined percentage of the network is infected? We
assume that nodes of different profiles can infect one another and we prove
that under realistic conditions, apart from the weak profile (great
sensitivity), the stronger profile (low sensitivity) will get infected as well.
First, we focus on cliques with the goal to provide exact theoretical results
as well as to get some intuition as to how a virus affects such a multiple
profile network. Then, we move to the theoretical analysis of arbitrary
networks. We provide bounds on certain properties of the network based on the
probabilities of infection of each node in it when it reaches the steady state.
Finally, we provide extensive experimental results that verify our theoretical
results and at the same time provide more insight on the problem
- …