Related papers: Exploring complex networks via topological embeddi…
We study spatial embeddings of random graphs in which nodes are randomly distributed in geographical space. We let the edge probability between any two nodes to be dependent on the spatial distance between them and demonstrate that this…
We study the behavior of the clustering coefficient in tagged networks. The rich variety of tags associated with the nodes in the studied systems provide additional information about the entities represented by the nodes which can be…
Higher-order connectivity patterns such as small induced sub-graphs called graphlets (network motifs) are vital to understand the important components (modules/functional units) governing the configuration and behavior of complex networks.…
Graph embedding provides an efficient solution for graph analysis by converting the graph into a low-dimensional space which preserves the structure information. In contrast to the graph structure data, the i.i.d. node embedding can be…
Computing the embedding distribution of a given graph is a fundamental question in topological graph theory. In this article, we extend our viewpoint to a sequence of graphs and consider their asymptotic embedding distributions, which are…
In machine learning, graph embedding algorithms seek low-dimensional representations of the input network data, thereby allowing for downstream tasks on compressed encodings. Recently, within the framework of network renormalization,…
We study collaboration networks in terms of evolving, self-organizing bipartite graph models. We propose a model of a growing network, which combines preferential edge attachment with the bipartite structure, generic for collaboration…
Graphs are commonly used to characterise interactions between objects of interest. Because they are based on a straightforward formalism, they are used in many scientific fields from computer science to historical sciences. In this paper,…
The value of graph-based big data can be unlocked by exploring the topology and metrics of the networks they represent, and the computational approaches to this exploration take on many forms. The use-case of performing global computations…
We present a graph theory-based method to characterise flow defects and structural shifts in condensed matter. We explore the connection between dynamical properties, particularly the recently introduced concept of ''softness'', and…
Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…
Real data collected from different applications that have additional topological structures and connection information are amenable to be represented as a weighted graph. Considering the node labeling problem, Graph Neural Networks (GNNs)…
Inferring topological characteristics of complex networks from observed data is critical to understand the dynamical behavior of networked systems, ranging from the Internet and the World Wide Web to biological networks and social networks.…
An embedding of a graph on a translation surface is said to be \emph{systolic} if each vertex of the graph corresponds to a singular point (or marked point) and each edge corresponds to a shortest saddle connection on the translation…
As one of the main subjects of investigation in data science, network science has been demonstrated a wide range of applications to real-world networks analysis and modeling. For example, the pervasive presence of structural or topological…
This work studies certain aspects of graphs embedded on surfaces. Initially, a colored graph model for a map of a graph on a surface is developed. Then, a concept analogous to (and extending) planar graph is introduced in the same spirit as…
An ordinary voltage graph embedding of a graph in a surface encodes a certain kind of highly symmetric covering space of that surface. Given an ordinary voltage graph embedding of a graph $G$ in a surface with voltage group $A$ and a…
It has been recently shown that any graph of genus g>0 can be stochastically embedded into a distribution over planar graphs, with distortion Olog (g+1)) [Sidiropoulos, FOCS 2010]. This embedding can be computed in polynomial time, provided…
The study of time-varying (dynamic) networks (graphs) is of fundamental importance for computer network analytics. Several methods have been proposed to detect the effect of significant structural changes in a time series of graphs. The…
Node-link diagrams are widely used to visualize graphs. Most graph layout algorithms only use graph topology for aesthetic goals (e.g., minimize node occlusions and edge crossings) or use node attributes for exploration goals (e.g.,…