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Bobkov, Houdr\'e, and the last author [2000] introduced a Poincar\'e-type functional parameter, $\lambda_\infty$, of a graph and related it to connectivity of the graph via Cheeger-type inequalities. A work by the second author,…
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…
Graph Neural Networks (GNNs) have become the standard approach for learning and reasoning over relational data, leveraging the message-passing mechanism that iteratively propagates node embeddings through graph structures. While GNNs have…
Virtual network services that span multiple data centers are important to support emerging data-intensive applications in fields such as bioinformatics and retail analytics. Successful virtual network service composition and maintenance…
Many real-world and artificial systems and processes can be represented as graphs. Some examples of such systems include social networks, financial transactions, supply chains, and molecular structures. In many of these cases, one needs to…
Many problems such as node classification and link prediction in network data can be solved using graph embeddings. However, it is difficult to use graphs to capture non-binary relations such as communities of nodes. These kinds of complex…
Recently, there has been increasing interest and progress in improvising the approximation algorithm for well-known NP-Complete problems, particularly the approximation algorithm for the Vertex-Cover problem. Here we have proposed a…
Graph matching refers to finding node correspondence between graphs, such that the corresponding node and edge's affinity can be maximized. In addition with its NP-completeness nature, another important challenge is effective modeling of…
The network embedding problem that maps nodes in a graph to vectors in Euclidean space can be very useful for addressing several important tasks on a graph. Recently, graph neural networks (GNNs) have been proposed for solving such a…
Real-world social networks and digital platforms are comprised of individuals (nodes) that are linked to other individuals or entities through multiple types of relationships (links). Sub-networks of such a network based on each type of…
In the classical Node-Disjoint Paths (NDP) problem, the input consists of an undirected $n$-vertex graph $G$, and a collection $\mathcal{M}=\{(s_1,t_1),\ldots,(s_k,t_k)\}$ of pairs of its vertices, called source-destination, or demand,…
Existing VM placement schemes have measured their effectiveness solely by looking either Physical Machine's resources(CPU, memory) or network resource. However, real applications use all resource types to varying degrees. The result of…
We present VMap, a map-like rectangular space-filling visualization, to perform vertex-centric graph exploration. Existing visualizations have limited support for quality optimization among rectangular aspect ratios, vertex-edge…
Graph-based algorithms have demonstrated state-of-the-art performance in the nearest neighbor search (NN-Search) problem. These empirical successes urge the need for theoretical results that guarantee the search quality and efficiency of…
Vertex similarity is a major problem in network science with a wide range of applications. In this work we provide novel perspectives on finding (dis)similar vertices within a network and across two networks with the same number of vertices…
We consider the classic problem of Network Reliability. A network is given together with a source vertex, one or more target vertices, and probabilities assigned to each of the edges. Each edge appears in the network with its associated…
We study the Telephone Broadcasting problem in graphs with restricted structure. Given a designated source in an undirected graph, the goal is to disseminate a message to all vertices in the minimum number of rounds, where in each round…
Network virtualization allows cloud infrastructure providers to accommodate multiple virtual networks on a single physical network. However, mapping multiple virtual network resources to physical network components, called virtual network…
Graph node embedding aims at learning a vector representation for all nodes given a graph. It is a central problem in many machine learning tasks (e.g., node classification, recommendation, community detection). The key problem in graph…
We initiate the theoretical study of the problem of minimizing the size of an iBGP overlay in an Autonomous System (AS) in the Internet subject to a natural notion of correctness derived from the standard "hot-potato" routing rules. For…