4,440 research outputs found
A Faster Method to Estimate Closeness Centrality Ranking
Closeness centrality is one way of measuring how central a node is in the
given network. The closeness centrality measure assigns a centrality value to
each node based on its accessibility to the whole network. In real life
applications, we are mainly interested in ranking nodes based on their
centrality values. The classical method to compute the rank of a node first
computes the closeness centrality of all nodes and then compares them to get
its rank. Its time complexity is , where represents total
number of nodes, and represents total number of edges in the network. In
the present work, we propose a heuristic method to fast estimate the closeness
rank of a node in time complexity, where . We
also propose an extended improved method using uniform sampling technique. This
method better estimates the rank and it has the time complexity , where . This is an excellent improvement over the
classical centrality ranking method. The efficiency of the proposed methods is
verified on real world scale-free social networks using absolute and weighted
error functions
Average Distance Queries through Weighted Samples in Graphs and Metric Spaces: High Scalability with Tight Statistical Guarantees
The average distance from a node to all other nodes in a graph, or from a
query point in a metric space to a set of points, is a fundamental quantity in
data analysis. The inverse of the average distance, known as the (classic)
closeness centrality of a node, is a popular importance measure in the study of
social networks. We develop novel structural insights on the sparsifiability of
the distance relation via weighted sampling. Based on that, we present highly
practical algorithms with strong statistical guarantees for fundamental
problems. We show that the average distance (and hence the centrality) for all
nodes in a graph can be estimated using single-source
distance computations. For a set of points in a metric space, we show
that after preprocessing which uses distance computations we can compute
a weighted sample of size such that the average
distance from any query point to can be estimated from the distances
from to . Finally, we show that for a set of points in a metric
space, we can estimate the average pairwise distance using
distance computations. The estimate is based on a weighted sample of
pairs of points, which is computed using distance
computations. Our estimates are unbiased with normalized mean square error
(NRMSE) of at most . Increasing the sample size by a
factor ensures that the probability that the relative error exceeds
is polynomially small.Comment: 21 pages, will appear in the Proceedings of RANDOM 201
Generalized Erdos Numbers for network analysis
In this paper we consider the concept of `closeness' between nodes in a
weighted network that can be defined topologically even in the absence of a
metric. The Generalized Erd\H{o}s Numbers (GENs) satisfy a number of desirable
properties as a measure of topological closeness when nodes share a finite
resource between nodes as they are real-valued and non-local, and can be used
to create an asymmetric matrix of connectivities. We show that they can be used
to define a personalized measure of the importance of nodes in a network with a
natural interpretation that leads to a new global measure of centrality and is
highly correlated with Page Rank. The relative asymmetry of the GENs (due to
their non-metric definition) is linked also to the asymmetry in the mean first
passage time between nodes in a random walk, and we use a linearized form of
the GENs to develop a continuum model for `closeness' in spatial networks. As
an example of their practicality, we deploy them to characterize the structure
of static networks and show how it relates to dynamics on networks in such
situations as the spread of an epidemic
- …