33,077 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
Maximum Entropy Models of Shortest Path and Outbreak Distributions in Networks
Properties of networks are often characterized in terms of features such as
node degree distributions, average path lengths, diameters, or clustering
coefficients. Here, we study shortest path length distributions. On the one
hand, average as well as maximum distances can be determined therefrom; on the
other hand, they are closely related to the dynamics of network spreading
processes. Because of the combinatorial nature of networks, we apply maximum
entropy arguments to derive a general, physically plausible model. In
particular, we establish the generalized Gamma distribution as a continuous
characterization of shortest path length histograms of networks or arbitrary
topology. Experimental evaluations corroborate our theoretical results
A Quality and Cost Approach for Comparison of Small-World Networks
We propose an approach based on analysis of cost-quality tradeoffs for
comparison of efficiency of various algorithms for small-world network
construction. A number of both known in the literature and original algorithms
for complex small-world networks construction are shortly reviewed and
compared. The networks constructed on the basis of these algorithms have basic
structure of 1D regular lattice with additional shortcuts providing the
small-world properties. It is shown that networks proposed in this work have
the best cost-quality ratio in the considered class.Comment: 27 pages, 16 figures, 1 tabl
- …