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Suppose we are given an $n$-node, $m$-edge input graph $G$, and the goal is to compute a spanning subgraph $H$ on $O(n)$ edges. This can be achieved in linear $O(m + n)$ time via breadth-first search. But can we hope for \emph{sublinear}…
Causal graphs are commonly used to understand and model complex systems. Researchers often construct these graphs from different perspectives, leading to significant variations for the same problem. Comparing causal graphs is, therefore,…
A \emph{Stick graph} is an intersection graph of axis-aligned segments such that the left end-points of the horizontal segments and the bottom end-points of the vertical segments lie on a `ground line,' a line with slope $-1$. It is an open…
For graph classification tasks, many traditional kernel methods focus on measuring the similarity between graphs. These methods have achieved great success on resolving graph isomorphism problems. However, in some classification problems,…
Graphs, and sequences of growing graphs, can be used to specify the architecture of mathematical models in many fields including machine learning and computational science. Here we define structured graph "lineages" (ordered by level…
The problem of finding the connected components of a graph is considered. The algorithms addressed to solve the problem are used to solve such problems on graphs as problems of finding points of articulation, bridges, maximin bridge, etc. A…
Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…
Graph processing is used extensively in areas from social networking mining to web indexing. We demonstrate that the performance and dependability of such applications critically hinges on the graph data structure used, because a fixed,…
The construction of large-scale, low-latency networks becomes difficult as the number of nodes increases. In general, the way to construct a theoretically optimal solution is unknown. However, it is known that some methods can construct…
We give the first analysis of the computational complexity of {\it coalition structure generation over graphs}. Given an undirected graph $G=(N,E)$ and a valuation function $v:2^N\rightarrow\RR$ over the subsets of nodes, the problem is to…
Designing molecular structures with desired chemical properties is an essential task in drug discovery and material design. However, finding molecules with the optimized desired properties is still a challenging task due to combinatorial…
In this work we introduce a concept of complexity for undirected graphs in terms of the spectral analysis of the Laplacian operator defined by the incidence matrix of the graph. Precisely, we compute the norm of the vector of eigenvalues of…
A large number of real-world networks include multiple types of nodes and edges. Graph Neural Network (GNN) emerged as a deep learning framework to generate node and graph embeddings for downstream machine learning tasks. However, popular…
There has been an increased interest in applying machine learning techniques on relational structured-data based on an observed graph. Often, this graph is not fully representative of the true relationship amongst nodes. In these settings,…
A neighborhood graph, which represents the instances as vertices and their relations as weighted edges, is the basis of many semi-supervised and relational models for node labeling and link prediction. Most methods employ a sequential…
Statistical inference for exponential-family models of random graphs with dependent edges is challenging. We stress the importance of additional structure and show that additional structure facilitates statistical inference. A simple…
We provide a novel approach to construct generative models for graphs. Instead of using the traditional probabilistic models or deep generative models, we propose to instead find an algorithm that generates the data. We achieve this using…
Graph generation is a critical task in numerous domains, including molecular design and social network analysis, due to its ability to model complex relationships and structured data. While most modern graph generative models utilize…
A graph is a data structure composed of dots (i.e. vertices) and lines (i.e. edges). The dots and lines of a graph can be organized into intricate arrangements. The ability for a graph to denote objects and their relationships to one…
Large graphs can be found in a wide array of scientific fields ranging from sociology and biology to scientometrics and computer science. Their analysis is by no means a trivial task due to their sheer size and complex structure. Such…