Related papers: A Graph Minor Perspective to Multicast Network Cod…
Recent advances in the field of network embedding have shown the low-dimensional network representation is playing a critical role in network analysis. However, most of the existing principles of network embedding do not incorporate…
In this paper we introduce Neural Network Coding(NNC), a data-driven approach to joint source and network coding. In NNC, the encoders at each source and intermediate node, as well as the decoder at each destination node, are neural…
The network topology can be described by the number of nodes and the interconnections among them. The degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability…
In this paper, we study two applications of graph minor reduction. In the first part of the paper, we introduce a variant of the boxicity, called strong boxicity, where the rectangular representation satisfies an additional condition that…
This work examines the problem of graph learning over a diffusion network when data can be collected from a limited portion of the network (partial observability). The main question is to establish technical guarantees of consistent…
Graph Neural Networks (GNNs) have achieved strong results in molecular property prediction, but polymers present distinct challenges: labeled datasets are scarce and small (typically in the order of hundreds of polymers) due to the need for…
Designing algorithms that generate networks with a given degree sequence while varying both subgraph composition and distribution of subgraphs around nodes is an important but challenging research problem. Current algorithms lack control of…
The present paper is the first one in the sequence of papers about a simple class of {\em framed $4$-graphs}; the goal of the present paper is to collect some well-known results on planarity and to reformulate them in the language of {\em…
Mader proved that for every integer $t$ there is a smallest real number $c(t)$ such that any graph with average degree at least $c(t)$ must contain a $K_t$-minor. Fiorini, Joret, Theis and Wood conjectured that any graph with $n$ vertices…
Graph neural networks have been extensively studied for learning with inter-connected data. Despite this, recent evidence has revealed GNNs' deficiencies related to over-squashing, heterophily, handling long-range dependencies, edge…
The existence of considerable amount of redundancy in the Internet traffic at the packet level has stimulated the deployment of packet-level redundancy elimination techniques within the network by enabling network nodes to memorize data…
Network representation learning (also known as information network embedding) has been the central piece of research in social and information network analysis for the last couple of years. An information network can be viewed as a linked…
Complex systems of interacting components often can be modeled by a simple graph $\mathcal{G}$ that consists of a set of $n$ nodes and a set of $m$ edges. Such a graph can be represented by an adjacency matrix $A\in\R^{n\times n}$, whose…
In the past two decades, significant advances have been made in understanding the structural and functional properties of biological networks, via graph-theoretic analysis. In general, most graph-theoretic studies are conducted in the…
A ladder is a $2 \times k$ grid graph. When does a graph class $\mathcal{C}$ exclude some ladder as a minor? We show that this is the case if and only if all graphs $G$ in $\mathcal{C}$ admit a proper vertex coloring with a bounded number…
Network coding has been widely used as a technology to ensure efficient and reliable communication. The ability to recode packets at the intermediate nodes is a major benefit of network coding implementations. This allows the intermediate…
The reasoning process of Graph Neural Networks is complex and considered opaque, limiting trust in their predictions. To alleviate this issue, prior work has proposed concept-based explanations, extracted from clusters in the model's node…
In 2006 Bonato and Tardif posed the Tree Alternative Conjecture (TAC): the equivalence class of a tree under the embeddability relation is, up to isomorphism, either trivial or infinite. In 2022 LaFlamme, et al. provided a rigorous…
Graph embedding is a transformation of nodes of a network into a set of vectors. A good embedding should capture the underlying graph topology and structure, node-to-node relationship, and other relevant information about the graph, its…
The problem of counting occurrences of query graphs in a large data graph, known as subgraph counting, is fundamental to several domains such as genomics and social network analysis. Many important special cases (e.g. triangle counting)…