Related papers: Testing Graph Clusterability: Algorithms and Lower…
Testing graph cluster structure has been a central object of study in property testing since the foundational work of Goldreich and Ron [STOC'96] on expansion testing, i.e. the problem of distinguishing between a single cluster (an…
Analysis of higher-order organizations, usually small connected subgraphs called motifs, is a fundamental task on complex networks. This paper studies a new problem of testing higher-order clusterability: given query access to an undirected…
We study the problem of recognizing the cluster structure of a graph in the framework of property testing in the bounded degree model. Given a parameter $\varepsilon$, a $d$-bounded degree graph is defined to be $(k, \phi)$-clusterable, if…
In the framework of graph property testing, we study the problem of determining if a graph admits a cluster structure. We say that a graph is $(k, \phi)$-clusterable if it can be partitioned into at most $k$ parts such that each part has…
In the graph clustering problem with a planted solution, the input is a graph on $n$ vertices partitioned into $k$ clusters, and the task is to infer the clusters from graph structure. A standard assumption is that clusters induce…
Due to the massive size of modern network data, local algorithms that run in sublinear time for analyzing the cluster structure of the graph are receiving growing interest. Two typical examples are local graph clustering algorithms that…
We address the problem of designing a sublinear-time spectral clustering oracle for graphs that exhibit strong clusterability. Such graphs contain $k$ latent clusters, each characterized by a large inner conductance (at least $\varphi$) and…
$ \def\vecc#1{\boldsymbol{#1}} $We design a polynomial time algorithm that for any weighted undirected graph $G = (V, E,\vecc w)$ and sufficiently large $\delta > 1$, partitions $V$ into subsets $V_1, \ldots, V_h$ for some $h\geq 1$, such…
Measuring graph clustering quality remains an open problem. To address it, we introduce quality measures based on comparisons of intra- and inter-cluster densities, an accompanying statistical test of the significance of their differences…
We present a new approach for solving (minimum disagreement) correlation clustering that results in sublinear algorithms with highly efficient time and space complexity for this problem. In particular, we obtain the following algorithms for…
One of the most useful measures of cluster quality is the modularity of a partition, which measures the difference between the number of the edges joining vertices from the same cluster and the expected number of such edges in a random…
In graph property testing the task is to distinguish whether a graph satisfies a given property or is "far" from having that property, preferably with a sublinear query and time complexity. In this work we initiate the study of property…
In this article, we extend a statistical test of graph clusterability, the $\delta$ test, to directed graphs with no self loops. The $\delta$ test, originally designed for undirected graphs, is based on the premise that graphs with a…
Current modularity-based community detection algorithms attempt to find cluster memberships that maximize modularity within a fixed graph topology. Diverging from this conventional approach, our work introduces a novel strategy that employs…
We study the problem of graph clustering where the goal is to partition a graph into clusters, i.e. disjoint subsets of vertices, such that each cluster is well connected internally while sparsely connected to the rest of the graph. In…
The objective of clustering is to discover natural groups in datasets and to identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics of the data. The problem can be seen as…
Graphs have become increasingly popular in modeling structures and interactions in a wide variety of problems during the last decade. Graph-based clustering and semi-supervised classification techniques have shown impressive performance.…
Graph-based clustering has shown promising performance in many tasks. A key step of graph-based approach is the similarity graph construction. In general, learning graph in kernel space can enhance clustering accuracy due to the…
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…
Clustering a graph means identifying internally dense subgraphs which are only sparsely interconnected. Formalizations of this notion lead to measures that quantify the quality of a clustering and to algorithms that actually find…