Related papers: Model-free consistency of graph partitioning
Where graphs are used for modelling and specifying systems, consistency is an important concern. To be a valid model of a system, the graph structure must satisfy a number of constraints. To date, consistency has primarily been viewed as a…
The large amount of work on community detection and its applications leaves unaddressed one important question: the statistical validation of the results. In this paper we present a methodology able to clearly detect if the community…
Spectral clustering is a fundamental method for graph partitioning, but its reliance on eigenvector computation limits scalability to massive graphs. Classical sparsification methods preserve spectral properties by sampling edges…
The coexistence of sparsity and clustering (non-vanishing average fraction of triangles per node) is one of the few structural features that, irrespective of finer details, are ubiquitously observed across large real-world networks. This…
This work develops a flexible and mathematically sound framework for the design and analysis of graph scattering networks with variable branching ratios and generic functional calculus filters. Spectrally-agnostic stability guarantees for…
In this paper, we present a detailed analysis of the global clustering coefficient in scale-free graphs. Many observed real-world networks of diverse nature have a power-law degree distribution. Moreover, the observed degree distribution…
We establish a central limit theorem for the sum of $\epsilon$-independent random variables, extending both the classical and free probability setting. Central to our approach is the use of graphon limits to characterize the limiting…
Consistency is a key property of all statistical procedures analyzing randomly sampled data. Surprisingly, despite decades of work, little is known about consistency of most clustering algorithms. In this paper we investigate consistency of…
We present a model and analysis of an eventually consistent graph database where loosely cooperating servers accept concurrent updates to a partitioned, distributed graph. The model is high-fidelity and preserves design choices from…
We establish tightness of graph-based stochastic processes in the space $D[0+\epsilon,1-\epsilon]$ with $\epsilon >0$ that allows for discontinuities of the first kind. The graph-based stochastic processes are based on statistics…
Most methods proposed to uncover communities in complex networks rely on their structural properties. Here we introduce the stability of a network partition, a measure of its quality defined in terms of the statistical properties of a…
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…
We investigate how the graph topology influences the robustness to noise in undirected linear consensus networks. We measure the structural robustness by using the smallest possible value of steady state population variance of states under…
A popular approach to semi-supervised learning proceeds by endowing the input data with a graph structure in order to extract geometric information and incorporate it into a Bayesian framework. We introduce new theory that gives appropriate…
Graph parameters such as the clique number, the chromatic number, and the independence number are central in many areas, ranging from computer networks to linguistics to computational neuroscience to social networks. In particular, the…
A thorough discussion of the statistical ensemble of scale-free connected random tree graphs is presented. Methods borrowed from field theory are used to define the ensemble and to study analytically its properties. The ensemble is…
Introduced the quantitative measure of the structural complexity of the graph (complex network, etc.) based on a procedure similar to the renormalization process, considering the difference between actual and averaged graph structures on…
Let a graph be observed through a finite random sampling mechanism. Spectral methods are routinely applied to such graphs, yet their outputs are treated as deterministic objects. This paper develops finite-sample inference for spectral…
We study the richness of the ensemble of graphical structures (i.e., unlabeled graphs) of the one-dimensional random geometric graph model defined by $n$ nodes randomly scattered in $[0,1]$ that connect if they are within the connection…
We introduce an abstract framework for the study of clustering in metric graphs: after suitably metrising the space of graph partitions, we restrict Laplacians to the clusters thus arising and use their spectral gaps to define several…