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Statistical field theory methods have been very successful with a number of random graph and random matrix problems, but it is challenging to apply these methods to graphs with prescribed degree sequences due to the extensive number of…
Smoothing methods find signals in noisy data. A challenge for Statistical inference is the choice of smoothing parameter. SiZer addressed this challenge in one-dimension by detecting significant slopes across multiple scales, but was not a…
Graph learning is often a necessary step in processing or representing structured data, when the underlying graph is not given explicitly. Graph learning is generally performed centrally with a full knowledge of the graph signals, namely…
In complex networks, especially social networks, networks could be divided into disjoint partitions that the ratio between the number of internal edges (the edges between the vertices within same partition) to the number of outer edges…
Detecting the dimensionality of graphs is a central topic in machine learning. While the problem has been tackled empirically as well as theoretically, existing methods have several drawbacks. On the one hand, empirical tools are…
Subgraph densities play a crucial role in network analysis, especially for the identification and interpretation of meaningful substructures in complex graphs. Localized subgraph densities, in particular, can provide valuable insights into…
Graph Neural Network (GNN) has demonstrated extraordinary performance in classifying graph properties. However, due to the selection bias of training and testing data (e.g., training on small graphs and testing on large graphs, or training…
Probabilistic dependency graphs (PDGs) are a flexible class of probabilistic graphical models, subsuming Bayesian Networks and Factor Graphs. They can also capture inconsistent beliefs, and provide a way of measuring the degree of this…
A split graph is a graph whose vertex set can be partitioned into a clique and a stable set. Given a graph $G$ and weight function $w: V(G) \to \mathbb{Q}_{\geq 0}$, the Split Vertex Deletion (SVD) problem asks to find a minimum weight set…
In classic distributed graph problems, each instance on a graph specifies a space of feasible solutions (e.g. all proper ($\Delta+1$)-list-colorings of the graph), and the task of distributed algorithm is to construct a feasible solution…
In the last decades, the study of models for large real-world networks has been a very popular and active area of research. A reasonable model should not only replicate all the structural properties that are observed in real world networks…
Self-supervised learning has gradually emerged as a powerful technique for graph representation learning. However, transferable, generalizable, and robust representation learning on graph data still remains a challenge for pre-training…
Exponential random graph models are an important tool in the statistical analysis of data. However, Bayesian parameter estimation for these models is extremely challenging, since evaluation of the posterior distribution typically involves…
The number of triangles in a graph is useful to deduce a plethora of important features of the network that the graph is modeling. However, finding the exact value of this number is computationally expensive. Hence, a number of…
Processing large complex networks like social networks or web graphs has recently attracted considerable interest. In order to do this in parallel, we need to partition them into pieces of about equal size. Unfortunately, previous parallel…
Analyzing large graph data is an essential part of many modern applications, such as social networks. Due to its large computational complexity, distributed processing is frequently employed. This requires graph data to be divided across…
We study the complexity of local graph centrality estimation, with the goal of approximating the centrality score of a given target node while exploring only a sublinear number of nodes/arcs of the graph and performing a sublinear number of…
A network can be analyzed at different topological scales, ranging from single nodes to motifs, communities, up to the complete structure. We propose a novel intermediate-level topological analysis that considers non-overlapping subgraphs…
Betweenness is a well-known centrality measure that ranks the nodes of a network according to their participation in shortest paths. Since an exact computation is prohibitive in large networks, several approximation algorithms have been…
We study a number of graph exploration problems in the following natural scenario: an algorithm starts exploring an undirected graph from some seed node; the algorithm, for an arbitrary node $v$ that it is aware of, can ask an oracle to…