62,057 research outputs found
Discriminative Distance-Based Network Indices with Application to Link Prediction
In large networks, using the length of shortest paths as the distance measure
has shortcomings. A well-studied shortcoming is that extending it to
disconnected graphs and directed graphs is controversial. The second
shortcoming is that a huge number of vertices may have exactly the same score.
The third shortcoming is that in many applications, the distance between two
vertices not only depends on the length of shortest paths, but also on the
number of shortest paths. In this paper, first we develop a new distance
measure between vertices of a graph that yields discriminative distance-based
centrality indices. This measure is proportional to the length of shortest
paths and inversely proportional to the number of shortest paths. We present
algorithms for exact computation of the proposed discriminative indices.
Second, we develop randomized algorithms that precisely estimate average
discriminative path length and average discriminative eccentricity and show
that they give -approximations of these indices. Third, we
perform extensive experiments over several real-world networks from different
domains. In our experiments, we first show that compared to the traditional
indices, discriminative indices have usually much more discriminability. Then,
we show that our randomized algorithms can very precisely estimate average
discriminative path length and average discriminative eccentricity, using only
few samples. Then, we show that real-world networks have usually a tiny average
discriminative path length, bounded by a constant (e.g., 2). Fourth, in order
to better motivate the usefulness of our proposed distance measure, we present
a novel link prediction method, that uses discriminative distance to decide
which vertices are more likely to form a link in future, and show its superior
performance compared to the well-known existing measures
SIR epidemics with long range infection in one dimension
We study epidemic processes with immunization on very large 1-dimensional
lattices, where at least some of the infections are non-local, with rates
decaying as power laws p(x) ~ x^{-sigma-1} for large distances x. When starting
with a single infected site, the cluster of infected sites stays always bounded
if (and dies with probability 1, of its size is allowed to
fluctuate down to zero), but the process can lead to an infinite epidemic for
sigma <1. For sigma <0 the behavior is essentially of mean field type, but for
0 < sigma <= 1 the behavior is non-trivial, both for the critical and for
supercritical cases. For critical epidemics we confirm a previous prediction
that the critical exponents controlling the correlation time and the
correlation length are simply related to each other, and we verify detailed
field theoretic predictions for sigma --> 1/3. For sigma = 1 we find generic
power laws with continuously varying exponents even in the supercritical case,
and confirm in detail the predicted Kosterlitz-Thouless nature of the
transition. Finally, the mass N(t) of supercritical clusters seems to grow for
0 < sigma < 1 like a stretched exponential. The latter implies that networks
embedded in 1-d space with power-behaved link distributions have infinite
intrinsic dimension (based on the graph distance), but are not small world.Comment: 16 pages, including 28 figures; minor changes from version v
Maximizing Friend-Making Likelihood for Social Activity Organization
The social presence theory in social psychology suggests that
computer-mediated online interactions are inferior to face-to-face, in-person
interactions. In this paper, we consider the scenarios of organizing in person
friend-making social activities via online social networks (OSNs) and formulate
a new research problem, namely, Hop-bounded Maximum Group Friending (HMGF), by
modeling both existing friendships and the likelihood of new friend making. To
find a set of attendees for socialization activities, HMGF is unique and
challenging due to the interplay of the group size, the constraint on existing
friendships and the objective function on the likelihood of friend making. We
prove that HMGF is NP-Hard, and no approximation algorithm exists unless P =
NP. We then propose an error-bounded approximation algorithm to efficiently
obtain the solutions very close to the optimal solutions. We conduct a user
study to validate our problem formulation and per- form extensive experiments
on real datasets to demonstrate the efficiency and effectiveness of our
proposed algorithm
Opinion and community formation in coevolving networks
In human societies opinion formation is mediated by social interactions,
consequently taking place on a network of relationships and at the same time
influencing the structure of the network and its evolution. To investigate this
coevolution of opinions and social interaction structure we develop a dynamic
agent-based network model, by taking into account short range interactions like
discussions between individuals, long range interactions like a sense for
overall mood modulated by the attitudes of individuals, and external field
corresponding to outside influence. Moreover, individual biases can be
naturally taken into account. In addition the model includes the opinion
dependent link-rewiring scheme to describe network topology coevolution with a
slower time scale than that of the opinion formation. With this model
comprehensive numerical simulations and mean field calculations have been
carried out and they show the importance of the separation between fast and
slow time scales resulting in the network to organize as well-connected small
communities of agents with the same opinion.Comment: 10 pages, 5 figures. New inset for Fig. 1 and references added.
Submitted to Physical Review
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