57,729 research outputs found
Revisiting Interval Graphs for Network Science
The vertices of an interval graph represent intervals over a real line where
overlapping intervals denote that their corresponding vertices are adjacent.
This implies that the vertices are measurable by a metric and there exists a
linear structure in the system. The generalization is an embedding of a graph
onto a multi-dimensional Euclidean space and it was used by scientists to study
the multi-relational complexity of ecology. However the research went out of
fashion in the 1980s and was not revisited when Network Science recently
expressed interests with multi-relational networks known as multiplexes. This
paper studies interval graphs from the perspective of Network Science
Affinity Paths and Information Diffusion in Social Networks
Widespread interest in the diffusion of information through social networks
has produced a large number of Social Dynamics models. A majority of them use
theoretical hypothesis to explain their diffusion mechanisms while the few
empirically based ones average out their measures over many messages of
different content. Our empirical research tracking the step-by-step email
propagation of an invariable viral marketing message delves into the content
impact and has discovered new and striking features. The topology and dynamics
of the propagation cascades display patterns not inherited from the email
networks carrying the message. Their disconnected, low transitivity, tree-like
cascades present positive correlation between their nodes probability to
forward the message and the average number of neighbors they target and show
increased participants' involvement as the propagation paths length grows. Such
patterns not described before, nor replicated by any of the existing models of
information diffusion, can be explained if participants make their pass-along
decisions based uniquely on local knowledge of their network neighbors affinity
with the message content. We prove the plausibility of such mechanism through a
stylized, agent-based model that replicates the \emph{Affinity Paths} observed
in real information diffusion cascades.Comment: 11 pages, 7 figure
Pioneers of Influence Propagation in Social Networks
With the growing importance of corporate viral marketing campaigns on online
social networks, the interest in studies of influence propagation through
networks is higher than ever. In a viral marketing campaign, a firm initially
targets a small set of pioneers and hopes that they would influence a sizeable
fraction of the population by diffusion of influence through the network. In
general, any marketing campaign might fail to go viral in the first try. As
such, it would be useful to have some guide to evaluate the effectiveness of
the campaign and judge whether it is worthy of further resources, and in case
the campaign has potential, how to hit upon a good pioneer who can make the
campaign go viral. In this paper, we present a diffusion model developed by
enriching the generalized random graph (a.k.a. configuration model) to provide
insight into these questions. We offer the intuition behind the results on this
model, rigorously proved in Blaszczyszyn & Gaurav(2013), and illustrate them
here by taking examples of random networks having prototypical degree
distributions - Poisson degree distribution, which is commonly used as a kind
of benchmark, and Power Law degree distribution, which is normally used to
approximate the real-world networks. On these networks, the members are assumed
to have varying attitudes towards propagating the information. We analyze three
cases, in particular - (1) Bernoulli transmissions, when a member influences
each of its friend with probability p; (2) Node percolation, when a member
influences all its friends with probability p and none with probability 1-p;
(3) Coupon-collector transmissions, when a member randomly selects one of his
friends K times with replacement. We assume that the configuration model is the
closest approximation of a large online social network, when the information
available about the network is very limited. The key insight offered by this
study from a firm's perspective is regarding how to evaluate the effectiveness
of a marketing campaign and do cost-benefit analysis by collecting relevant
statistical data from the pioneers it selects. The campaign evaluation
criterion is informed by the observation that if the parameters of the
underlying network and the campaign effectiveness are such that the campaign
can indeed reach a significant fraction of the population, then the set of good
pioneers also forms a significant fraction of the population. Therefore, in
such a case, the firms can even adopt the naive strategy of repeatedly picking
and targeting some number of pioneers at random from the population. With this
strategy, the probability of them picking a good pioneer will increase
geometrically fast with the number of tries
Dynamical Properties of Interaction Data
Network dynamics are typically presented as a time series of network
properties captured at each period. The current approach examines the dynamical
properties of transmission via novel measures on an integrated, temporally
extended network representation of interaction data across time. Because it
encodes time and interactions as network connections, static network measures
can be applied to this "temporal web" to reveal features of the dynamics
themselves. Here we provide the technical details and apply it to agent-based
implementations of the well-known SEIR and SEIS epidemiological models.Comment: 29 pages, 15 figure
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