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Graph data widely exist in many high-impact applications. Inspired by the success of deep learning in grid-structured data, graph neural network models have been proposed to learn powerful node-level or graph-level representation. However,…
Exploring small connected and induced subgraph patterns (CIS patterns, or graphlets) has recently attracted considerable attention. Despite recent efforts on computing the number of instances a specific graphlet appears in a large graph…
Threshold graphs are a prevalent and widely studied class of simple graphs. They have several equivalent definitions which makes them a go-to class for finding examples and counter examples when testing and learning. This versatility has…
We initiate the study of property testing in arbitrary planar graphs. We prove that bipartiteness can be tested in constant time, improving on the previous bound of $\tilde{O}(\sqrt{n})$ for graphs on $n$ vertices. The constant-time…
We study the asymptotics of large directed graphs, constrained to have certain densities of edges and/or outward $p$-stars. Our models are close cousins of exponential random graph models (ERGMs), in which edges and certain other subgraph…
Graph-modification problems, where we modify a graph by adding or deleting vertices or edges or contracting edges to obtain a graph in a {\it simpler} class, is a well-studied optimization problem in all algorithmic paradigms including…
Theory of graphical models has matured over more than three decades to provide the backbone for several classes of models that are used in a myriad of applications such as genetic mapping of diseases, credit risk evaluation, reliability and…
Graph classification has practical applications in diverse fields. Recent studies show that graph-based machine learning models are especially vulnerable to adversarial perturbations due to the non i.i.d nature of graph data. By adding or…
Given a finite set of $2$-edge-coloured graphs $\mathcal F$ and a hereditary property of graphs $\mathcal{P}$, we say that $\mathcal F$ expresses $\mathcal{P}$ if a graph $G$ has the property $\mathcal{P}$ if and only if it admits a…
In this paper, we study the task of detecting the edge dependency between two weighted random graphs. We formulate this task as a simple hypothesis testing problem, where under the null hypothesis, the two observed graphs are statistically…
Suppose a graph has no large balanced bicliques, but has large minimum degree. Then what can we say about its induced subgraphs? This question motivates the study of degree-boundedness, which is like $\chi$-boundedness but for minimum…
Hypothesis testing for graphs has been an important tool in applied research fields for more than two decades, and still remains a challenging problem as one often needs to draw inference from few replicates of large graphs. Recent studies…
These lecture notes are a personal introduction to signed graphs, concentrating on the aspects that have been most persistently interesting to me. They are just a few corners of signed graph theory; I am leaving out a great deal. The…
Limits of graphs were initiated recently in the two extreme contexts of dense and bounded degree graphs. This led to elegant limiting structures called graphons and graphings. These approach have been unified and generalized by authors in a…
Graph-structured data appears frequently in domains including chemistry, natural language semantics, social networks, and knowledge bases. In this work, we study feature learning techniques for graph-structured inputs. Our starting point is…
Gurski and Wanke showed that a graph class C has bounded tree-width if and only if its associated class of directed line graphs has bounded clique-width. Inevitably -- asking whether this relationship lifts to directed graphs -- we…
Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have…
We present new families of goodness-of-fit tests of uniformity on a full-dimensional set $W\subset\R^d$ based on statistics related to edge lengths of random geometric graphs. Asymptotic normality of these statistics is proven under the…
Like Graph Neural Networks (GNNs), Signed Graph Neural Networks (SGNNs) are also up against fairness issues from source data and typical aggregation method. In this paper, we are pioneering to make the investigation of fairness in SGNNs…
In this paper, we use the concept of colored edge graphs to model homogeneous faults in networks. We then use this model to study the minimum connectivity (and design) requirements of networks for being robust against homogeneous faults…