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A large portion of today's big data can be represented as networks. However, not all networks are the same, and in fact, for many that have additional complexities to their structure, traditional general network analysis methods are no…
The collection of data on populations of networks is becoming increasingly common, where each data point can be seen as a realisation of a network-valued random variable. A canonical example is that of brain networks: a typical neuroimaging…
Random graph (RG) models play a central role in the complex networks analysis. They help to understand, control, and predict phenomena occurring, for instance, in social networks, biological networks, the Internet, etc. Despite a large…
The study of evolution of networks has received increased interest with the recent discovery that many real-world networks possess many things in common, in particular the manner of evolution of such networks. By adding a dimension of time…
A number of real-world networks are, in fact, one-mode projections of bipartite networks comprised of two types of nodes. For institutions engaging in collaboration for technological innovation, the underlying network is bipartite with…
Hypergraphs are a powerful abstraction for representing higher-order interactions between entities of interest. To exploit these relationships in making downstream predictions, a variety of hypergraph neural network architectures have…
In an increasingly interconnected world, understanding and summarizing the structure of these networks becomes increasingly relevant. However, this task is nontrivial; proposed summary statistics are as diverse as the networks they…
We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows the for the generation of…
The Random Geometric Graph (RGG) is a random graph model for network data with an underlying spatial representation. Geometry endows RGGs with a rich dependence structure and often leads to desirable properties of real-world networks such…
Network dynamics may be viewed as a process of change in the edge structure of a network, in the vertex set on which edges are defined, or in both simultaneously. Though early studies of such processes were primarily descriptive, recent…
Cycles are fundamental elements in graph-structured data and have demonstrated their effectiveness in enhancing graph learning models. To encode such information into a graph learning framework, prior works often extract a summary quantity,…
Consider a graph with $n$ vertices where the shortest odd cycle is of length $>2k+1$. We revisit two known results about such graphs: (I) Such a graph is almost bipartite, in the sense that it can be made bipartite by removing from it…
The aim of this paper is to extend and generalise some work of Katona on the existence of perfect matchings or Hamilton cycles in graphs subject to certain constraints. The most general form of these constraints is that we are given a…
Bipartite networks provide an insightful representation of many systems, ranging from mutualistic networks of species interactions to investment networks in finance. The analysis of their topological structures has revealed the ubiquitous…
We use a tensor unfolding technique to prove a new identifiability result for discrete bipartite graphical models, which have a bipartite graph between an observed and a latent layer. This model family includes popular models such as…
A number of recent works have used a variety of combinatorial constructions to derive Tanner graphs for LDPC codes and some of these have been shown to perform well in terms of their probability of error curves and error floors. Such graphs…
We analyse the bipartite dynamic network of inventors and patents registered within the main area of electrical engineering in Germany to explore the driving forces behind innovation. The data at hand leads to a bipartite network, where an…
Signed networks are such social networks having both positive and negative links. A lot of theories and algorithms have been developed to model such networks (e.g., balance theory). However, previous work mainly focuses on the unipartite…
Let $G=(U \cup V, E)$ be a bipartite graph, where $U$ represents jobs and $V$ represents machines. We study a new variant of the bipartite matching problem in which each job in $U$ can be matched to at most one machine in $V$, and the…
We study the family of network models derived by requiring the expected properties of a graph ensemble to match a given set of measurements of a real-world network, while maximizing the entropy of the ensemble. Models of this type play the…