Related papers: Exploring complex networks via topological embeddi…
We show how, given a sufficiently large point cloud sampled from an embedded 2-manifold in $\mathbb{R}^n$, we may obtain a global representation as a cell complex with vertices given by a representative subset of the point cloud. The vertex…
Biomedical networks (or graphs) are universal descriptors for systems of interacting elements, from molecular interactions and disease co-morbidity to healthcare systems and scientific knowledge. Advances in artificial intelligence,…
Nodes residing in different parts of a graph can have similar structural roles within their local network topology. The identification of such roles provides key insight into the organization of networks and can be used for a variety of…
Learning embeddings from large-scale networks is an open challenge. Despite the overwhelming number of existing methods, is is unclear how to exploit network structure in a way that generalizes easily to unseen nodes, edges or graphs. In…
Graph Neural Networks (GNNs) have achieved a lot of success with graph-structured data. However, it is observed that the performance of GNNs does not improve (or even worsen) as the number of layers increases. This effect has known as…
Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In…
When analyzing weighted networks using spectral embedding, a judicious transformation of the edge weights may produce better results. To formalize this idea, we consider the asymptotic behavior of spectral embedding for different…
Given a `genus' function $g=g(n)$, we let $\mathcal{E}^g$ be the class of all graphs $G$ such that if $G$ has order $n$ (that is, has $n$ vertices) then it is embeddable in a surface of Euler genus at most $g(n)$. Let the random graph $R_n$…
We propose a novel method for topological analysis of unweighted graphs which is based on \textit{persistent homology}. The proposed method maps the input graph to a complete weighted graph where the weighting function maps each edge to a…
A significant portion of the data today, e.g, social networks, web connections, etc., can be modeled by graphs. A proper analysis of graphs with Machine Learning (ML) algorithms has the potential to yield far-reaching insights into many…
Feature extraction and dimension reduction for networks is critical in a wide variety of domains. Efficiently and accurately learning features for multiple graphs has important applications in statistical inference on graphs. We propose a…
The main paradigm of smoothed analysis on graphs suggests that for any large graph $G$ in a certain class of graphs, perturbing slightly the edges of $G$ at random (usually adding few random edges to $G$) typically results in a graph having…
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…
A method for embedding graphs in Euclidean space is suggested. The method connects nodes to their geographically closest neighbors and economizes on the total physical length of links. The topological and geometrical properties of…
Due to the advent of the expressions of data other than tabular formats, the topological compositions which make samples interrelated came into prominence. Analogically, those networks can be interpreted as social connections, dataflow…
Graph embedding aims at learning a vector-based representation of vertices that incorporates the structure of the graph. This representation then enables inference of graph properties. Existing graph embedding techniques, however, do not…
Graph neural networks (GNNs) have demonstrated a significant success in various graph learning tasks, from graph classification to anomaly detection. There recently has emerged a number of approaches adopting a graph pooling operation…
Lying at the interface between Network Science and Machine Learning, node embedding algorithms take a graph as input and encode its structure onto output vectors that represent nodes in an abstract geometric space, enabling various…
Mining graph data has become a popular research topic in computer science and has been widely studied in both academia and industry given the increasing amount of network data in the recent years. However, the huge amount of network data…
Compound graphs are networks in which vertices can be grouped into larger subsets, with these subsets capable of further grouping, resulting in a nesting that can be many levels deep. In several applications, including biological workflows,…