6,567 research outputs found
Edge Label Inference in Generalized Stochastic Block Models: from Spectral Theory to Impossibility Results
The classical setting of community detection consists of networks exhibiting
a clustered structure. To more accurately model real systems we consider a
class of networks (i) whose edges may carry labels and (ii) which may lack a
clustered structure. Specifically we assume that nodes possess latent
attributes drawn from a general compact space and edges between two nodes are
randomly generated and labeled according to some unknown distribution as a
function of their latent attributes. Our goal is then to infer the edge label
distributions from a partially observed network. We propose a computationally
efficient spectral algorithm and show it allows for asymptotically correct
inference when the average node degree could be as low as logarithmic in the
total number of nodes. Conversely, if the average node degree is below a
specific constant threshold, we show that no algorithm can achieve better
inference than guessing without using the observations. As a byproduct of our
analysis, we show that our model provides a general procedure to construct
random graph models with a spectrum asymptotic to a pre-specified eigenvalue
distribution such as a power-law distribution.Comment: 17 page
Non-parametric resampling of random walks for spectral network clustering
Parametric resampling schemes have been recently introduced in complex
network analysis with the aim of assessing the statistical significance of
graph clustering and the robustness of community partitions. We propose here a
method to replicate structural features of complex networks based on the
non-parametric resampling of the transition matrix associated with an unbiased
random walk on the graph. We test this bootstrapping technique on synthetic and
real-world modular networks and we show that the ensemble of replicates
obtained through resampling can be used to improve the performance of standard
spectral algorithms for community detection.Comment: 5 pages, 2 figure
Recommended from our members
Community detection in network analysis: a survey
The existence of community structures in networks is not unusual, including in the domains of sociology, biology, and business, etc. The characteristic of the community structure is that nodes of the same community are highly similar while on the contrary, nodes across communities present low similarity.
In academia, there is a surge in research efforts on community detection in network analysis, especially in developing statistically sound methodologies for exploring, modeling, and interpreting these kind of structures and relationships.
This survey paper aims to provide a brief review of current applicable
statistical methodologies and approaches in a comparative manner along with metrics for evaluating graph clustering results and application using R. At the
end, we provide promising future research directions.Statistic
Spectral Graph Forge: Graph Generation Targeting Modularity
Community structure is an important property that captures inhomogeneities
common in large networks, and modularity is one of the most widely used metrics
for such community structure. In this paper, we introduce a principled
methodology, the Spectral Graph Forge, for generating random graphs that
preserves community structure from a real network of interest, in terms of
modularity. Our approach leverages the fact that the spectral structure of
matrix representations of a graph encodes global information about community
structure. The Spectral Graph Forge uses a low-rank approximation of the
modularity matrix to generate synthetic graphs that match a target modularity
within user-selectable degree of accuracy, while allowing other aspects of
structure to vary. We show that the Spectral Graph Forge outperforms
state-of-the-art techniques in terms of accuracy in targeting the modularity
and randomness of the realizations, while also preserving other local
structural properties and node attributes. We discuss extensions of the
Spectral Graph Forge to target other properties beyond modularity, and its
applications to anonymization
Graph Summarization
The continuous and rapid growth of highly interconnected datasets, which are
both voluminous and complex, calls for the development of adequate processing
and analytical techniques. One method for condensing and simplifying such
datasets is graph summarization. It denotes a series of application-specific
algorithms designed to transform graphs into more compact representations while
preserving structural patterns, query answers, or specific property
distributions. As this problem is common to several areas studying graph
topologies, different approaches, such as clustering, compression, sampling, or
influence detection, have been proposed, primarily based on statistical and
optimization methods. The focus of our chapter is to pinpoint the main graph
summarization methods, but especially to focus on the most recent approaches
and novel research trends on this topic, not yet covered by previous surveys.Comment: To appear in the Encyclopedia of Big Data Technologie
- …