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Motivated by applications in social and biological network analysis, we introduce a new form of agnostic clustering termed~\emph{motif correlation clustering}, which aims to minimize the cost of clustering errors associated with both edges…
Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, and $f$ be a 0-1 labeling of $E(G)$ so that the absolute difference in the number of edges labeled 1 and 0 is no more than one. Call such a labeling $f$ \emph{edge-friendly}. We…
This paper studies the problem of detecting anomalous graphs using a machine learning model trained on only normal graphs, which has many applications in molecule, biology, and social network data analysis. We present a self-discriminative…
We investigate the asymptotic number of induced subgraphs in power-law uniform random graphs. We show that these induced subgraphs appear typically on vertices with specific degrees, which are found by solving an optimization problem.…
Deep learning models have achieved huge success in numerous fields, such as computer vision and natural language processing. However, unlike such fields, it is hard to apply traditional deep learning models on the graph data due to the…
In this letter, we propose an algorithm for learning a sparse weighted graph by estimating its adjacency matrix under the assumption that the observed signals vary smoothly over the nodes of the graph. The proposed algorithm is based on the…
Classical graph matching aims to find a node correspondence between two unlabeled graphs of known topologies. This problem has a wide range of applications, from matching identities in social networks to identifying similar biological…
Graph embedding, representing local and global neighborhood information by numerical vectors, is a crucial part of the mathematical modeling of a wide range of real-world systems. Among the embedding algorithms, random walk-based algorithms…
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.…
In machine learning, classifiers are typically susceptible to noise in the training data. In this work, we aim at reducing intra-class noise with the help of graph filtering to improve the classification performance. Considered graphs are…
An adjacency labeling scheme is a method that assigns labels to the vertices of a graph such that adjacency between vertices can be inferred directly from the assigned label, without using a centralized data structure. We devise adjacency…
The isomorphism problem is known to be efficiently solvable for interval graphs, while for the larger class of circular-arc graphs its complexity status stays open. We consider the intermediate class of intersection graphs for families of…
A seminal palette sparsification result of Assadi, Chen, and Khanna states that in every $n$-vertex graph of maximum degree $\Delta$, sampling $\Theta(\log n)$ colors per vertex from $\{1, \ldots, \Delta+1\}$ almost certainly allows for a…
Two landmark results in combinatorial random matrix theory, due to Koml\'os and Costello-Tao-Vu, show that discrete random matrices and symmetric discrete random matrices are typically nonsingular. In particular, in the language of graph…
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…
Graph labelling is one of the noticed contexts in combinatorics and graph theory. Graceful labelling for a graph $G$ with $e$ edges, is to label the vertices of $G$ with $0, 1, \cdots, e$ such that, if we specify to each edge the difference…
In graph sparsification, the goal has almost always been of {global} nature: compress a graph into a smaller subgraph ({sparsifier}) that maintains certain features of the original graph. Algorithms can then run on the sparsifier, which in…
The prime graph of a finite group $G$ is the labelled graph $\Gamma(G)$ with vertices the prime divisors of $|G|$ and edges the pairs $\{p,q\}$ for which $G$ contains an element of order $pq$. A group $G$ is recognisable by its prime graph…
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…
We present the analysis of the topological graph descriptor Local Degree Profile (LDP), which forms a widely used structural baseline for graph classification. Our study focuses on model evaluation in the context of the recently developed…