Related papers: Weighted Spectral Embedding of Graphs
Graph embeddings, wherein the nodes of the graph are represented by points in a continuous space, are used in a broad range of Graph ML applications. The quality of such embeddings crucially depends on whether the geometry of the space…
Spectral graph sparsification has emerged as a powerful tool in the analysis of large-scale networks by reducing the overall number of edges, while maintaining a comparable graph Laplacian matrix. In this paper, we present an efficient…
Spectral analysis of networks states that many structural properties of graphs, such as centrality of their nodes, are given in terms of their adjacency matrices. The natural extension of such spectral analysis to higher order networks is…
In this note we give a new upper bound for the Laplacian eigenvalues of an unweighted graph. Let $G$ be a simple graph on $n$ vertices. Let $d_{m}(G)$ and $\lambda_{m+1}(G)$ be the $m$-th smallest degree of $G$ and the $m+1$-th smallest…
We investigate combinatorial properties of certain configurations of a graph partition which are related to the minimality of a cut. We show that such configurations are related to the third eigenvector of the Laplacian matrix. It is well…
Consider the setting of \emph{randomly weighted graphs}, namely, graphs whose edge weights are chosen independently according to probability distributions with finite support over the non-negative reals. Under this setting, properties of…
Simplicial complexes are generalizations of graphs that describe higher-order network interactions among nodes in the graph. Network dynamics described by graph Laplacian flows have been widely studied in network science and control theory,…
Graph embedding techniques have been increasingly deployed in a multitude of different applications that involve learning on non-Euclidean data. However, existing graph embedding models either fail to incorporate node attribute information…
We study methods to manipulate weights in stress-graph embeddings to improve convex straight-line planar drawings of 3-connected planar graphs. Stress-graph embeddings are weighted versions of Tutte embeddings, where solving a linear system…
Graph alignment, the problem of identifying corresponding nodes across multiple graphs, is fundamental to numerous applications. Most existing unsupervised methods embed node features into latent representations to enable cross-graph…
Because of the significant increase in size and complexity of the networks, the distributed computation of eigenvalues and eigenvectors of graph matrices has become very challenging and yet it remains as important as before. In this paper…
Graph embedding aims to transfer a graph into vectors to facilitate subsequent graph analytics tasks like link prediction and graph clustering. Most approaches on graph embedding focus on preserving the graph structure or minimizing the…
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…
Recent works on representation learning for graph structured data predominantly focus on learning distributed representations of graph substructures such as nodes and subgraphs. However, many graph analytics tasks such as graph…
Finite order invariants (Vassiliev invariants) of knots are expressed in terms of weight systems, that is, functions on chord diagrams satisfying the four-term relations. Weight systems have graph analogues, so-called $4$-invariants of…
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…
What is the dimension of a network? Here, we view it as the smallest dimension of Euclidean space into which nodes can be embedded so that pairwise distances accurately reflect the connectivity structure. We show that a recently proposed…
Graph machine learning has been widely explored in various domains, such as community detection, transaction analysis, and recommendation systems. In these applications, anomaly detection plays an important role. Recently, studies have…
In this paper, we demonstrate a useful interaction between the theory of clique partitions, edge clique covers of a graph, and the spectra of graphs. Using a clique partition and an edge clique cover of a graph we introduce the notion of a…
Graph drawing research traditionally focuses on producing geometric embeddings of graphs satisfying various aesthetic constraints. After the geometric embedding is specified, there is an additional step that is often overlooked or ignored:…