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One of the most fundamental concepts in statistics is the concept of sample mean. Properties of the sample mean that are well-defined in Euclidean spaces become unwieldy or even unclear in graph spaces. Open problems related to the sample…
Graph embedding is a powerful method in parallel computing that maps a guest network $G$ into a host network $H$. The performance of an embedding can be evaluated by certain parameters, such as the dilation, the edge congestion and the…
Learning powerful data embeddings has become a center piece in machine learning, especially in natural language processing and computer vision domains. The crux of these embeddings is that they are pretrained on huge corpus of data in a…
Simultaneous embedding is concerned with simultaneously representing a series of graphs sharing some or all vertices. This forms the basis for the visualization of dynamic graphs and thus is an important field of research. Recently there…
Network (or graph) embedding is the task to map the nodes of a graph to a lower dimensional vector space, such that it preserves the graph properties and facilitates the downstream network mining tasks. Real world networks often come with…
We present an exact algorithm for computing all common subgraphs with the maximum number of vertices across multiple graphs. Our approach is further extended to handle the connected Maximum Common Subgraph (MCS), identifying the largest…
Graph embedding is a powerful method to represent graph neurological data (e.g., brain connectomes) in a low dimensional space for brain connectivity mapping, prediction and classification. However, existing embedding algorithms have two…
Unit disk graphs are the intersection graphs of unit radius disks in the Euclidean plane. Deciding whether there exists an embedding of a given unit disk graph, i.e. unit disk graph recognition, is an important geometric problem, and has…
Graph inference plays an essential role in machine learning, pattern recognition, and classification. Signal processing based approaches in literature generally assume some variational property of the observed data on the graph. We make a…
Graph embedding methods are becoming increasingly popular in the machine learning community, where they are widely used for tasks such as node classification and link prediction. Embedding graphs in geometric spaces should aid the…
Modern graph embedding procedures can efficiently process graphs with millions of nodes. In this paper, we propose GEMSEC -- a graph embedding algorithm which learns a clustering of the nodes simultaneously with computing their embedding.…
Node embedding algorithms produce low-dimensional latent representations of nodes in a graph. These embeddings are often used for downstream tasks, such as node classification and link prediction. In this paper, we investigate the following…
Betweenness centrality is a classic measure that quantifies the importance of a graph element (vertex or edge) according to the fraction of shortest paths passing through it. This measure is notoriously expensive to compute, and the best…
Distribution testing can be described as follows: $q$ samples are being drawn from some unknown distribution $P$ over a known domain $[n]$. After the sampling process, a decision must be made about whether $P$ holds some property, or is far…
Methods that learn representations of nodes in a graph play a critical role in network analysis since they enable many downstream learning tasks. We propose Graph2Gauss - an approach that can efficiently learn versatile node embeddings on…
The definition of $1$-planar graphs naturally extends graph planarity, namely a graph is $1$-planar if it can be drawn in the plane with at most one crossing per edge. Unfortunately, while testing graph planarity is solvable in linear time,…
Graph, as an important data representation, is ubiquitous in many real world applications ranging from social network analysis to biology. How to correctly and effectively learn and extract information from graph is essential for a large…
One of the important features of an interconnection network is its ability to efficiently simulate programs or parallel algorithms written for other architectures. Such a simulation problem can be mathematically formulated as a graph…
Graphlets are induced subgraphs of a large network and are important for understanding and modeling complex networks. Despite their practical importance, graphlets have been severely limited to applications and domains with relatively small…
The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…