Related papers: Forman-Ricci Curvature for Hypergraphs
Most graph neural networks (GNNs) use the message passing paradigm, in which node features are propagated on the input graph. Recent works pointed to the distortion of information flowing from distant nodes as a factor limiting the…
Rapid discovery of new reactions and molecules in recent years has been facilitated by the advancements in high throughput screening, accessibility to a much more complex chemical design space, and the development of accurate molecular…
Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic…
Many applications in network science have recently been discovered for the "curvature" of a network, but there is no consensus on the definition for this term. A common approach in these applications is to derive from the curvature either a…
The random walk is fundamental to modeling dynamic processes on networks. Metrics based on the random walk have been used in many applications from image processing to Web page ranking. However, how appropriate are random walks to modeling…
Introduced the quantitative measure of the structural complexity of the graph (complex network, etc.) based on a procedure similar to the renormalization process, considering the difference between actual and averaged graph structures on…
The structural analysis of shape boundaries leads to the characterization of objects as well as to the understanding of shape properties. The literature on graphs and networks have contributed to the structural characterization of shapes…
Graph Neural Networks (GNNs) have demonstrated strong representation learning capabilities for graph-based tasks. Recent advances on GNNs leverage geometric properties, such as curvature, to enhance its representation capabilities by…
In the continuum, close connections exist between mean curvature flow, the Allen-Cahn (AC) partial differential equation, and the Merriman-Bence-Osher (MBO) threshold dynamics scheme. Graph analogues of these processes have recently seen a…
Directed acyclic graphs are a fundamental class of networks that includes citation networks, food webs, and family trees, among others. Here we define a random graph model for directed acyclic graphs and give solutions for a number of the…
Modern sociology has profoundly uncovered many convincing social criteria for behavioural analysis. Unfortunately, many of them are too subjective to be measured and presented in online social networks. On the other hand, data mining…
Graph centrality measures use the structure of a network to quantify central or "important" nodes, with applications in web search, social media analysis, and graphical data mining generally. Traditional centrality measures such as the well…
$Anomaly$ $detection$ problems (also called $change$-$point$ $detection$ problems) have been studied in data mining, statistics and computer science over the last several decades in applications such as medical condition monitoring and…
Clique-width is a complexity measure of directed as well as undirected graphs. Rank-width is an equivalent complexity measure for undirected graphs and has good algorithmic and structural properties. It is in particular related to the…
RDF2vec is a technique for creating vector space embeddings from an RDF knowledge graph, i.e., representing each entity in the graph as a vector. It first creates sequences of nodes by performing random walks on the graph. In a second step,…
Hypergraphs are a generalization of graphs in which edges can connect any number of vertices. They allow the modeling of complex networks with higher-order interactions, and their spectral theory studies the qualitative properties that can…
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…
A wide variety of complex networks (social, biological, information etc.) exhibit local clustering with substantial variation in the clustering coefficient (the probability of neighbors being connected). Existing models of large graphs…
Generating computational anatomical models of cerebrovascular networks is vital for improving clinical practice and understanding brain oxygen transport. This is achieved by extracting graph-based representations based on pre-mapping of…
We study Riemannian manifolds with boundary under a lower weighted Ricci curvature bound. We consider a curvature condition in which the weighted Ricci curvature is bounded from below by the density function. Under the curvature condition,…