Related papers: The nature of hypergraph $k$-core percolation prob…
Hypergraphs naturally represent higher-order interactions, which persistently appear from social interactions to neural networks and other natural systems. Although their importance is well recognized, a theoretical framework to describe…
The richness of many complex systems stems from the interactions among their components. The higher-order nature of these interactions, involving many units at once, and their temporal dynamics constitute crucial properties that shape the…
Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…
Motivated by the increasing need for fast processing of large-scale graphs, we study a number of fundamental graph problems in a message-passing model for distributed computing, called $k$-machine model, where we have $k$ machines that…
Hypergraphs provide a natural way of representing group relations, whose complexity motivates an extensive array of prior work to adopt some form of abstraction and simplification of higher-order interactions. However, the following…
The physics of $k$-core percolation pertains to those systems whose constituents require a minimum number of $k$ connections to each other in order to participate in any clustering phenomenon. Examples of such a phenomenon range from…
We present the theory of the k-core pruning process (progressive removal of nodes with degree less than k) in uncorrelated random networks. We derive exact equations describing this process and the evolution of the network structure, and…
Multiplex networks describe a large variety of complex systems including infrastructures, transportation networks and biological systems. Most of these networks feature a significant link overlap. It is therefore of particular importance to…
There is increasing focus on analyzing data represented as hypergraphs, which are better able to express complex relationships amongst entities than are graphs. Much of the critical information about hypergraph structure is available only…
We study both numerically and analytically what happens to a random graph of average connectivity "alpha" when its leaves and their neighbors are removed iteratively up to the point when no leaf remains. The remnant is made of isolated…
Identifying cohesive subgraphs in hypergraphs is a fundamental problem that has received recent attention in data mining and engineering fields. Existing approaches mainly focus on a strongly induced subhypergraph or edge cardinality,…
We propose a new representation of $k$-partite, $k$-uniform hypergraphs, that is, a hypergraph with a partition of vertices into $k$ parts such that each hyperedge contains exactly one vertex of each type; we call them $k$-hypergraphs for…
In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially…
Recently, graph neural networks have attracted great attention and achieved prominent performance in various research fields. Most of those algorithms have assumed pairwise relationships of objects of interest. However, in many real…
We study the random graph obtained by random deletion of vertices or edges from a random graph with given vertex degrees. A simple trick of exploding vertices instead of deleting them, enables us to derive results from known results for…
(Hyper)Graph decomposition is a family of problems that aim to break down large (hyper)graphs into smaller sub(hyper)graphs for easier analysis. The importance of this lies in its ability to enable efficient computation on large and complex…
Hypergraphs are generalisation of graphs in which a hyperedge can connect any number of vertices. It can describe n-ary relationships and high-order information among entities compared to conventional graphs. In this paper, we study the…
Hypergraphs, increasingly utilised to model complex and diverse relationships in modern networks, have gained significant attention for representing intricate higher-order interactions. Among various challenges, cohesive subgraph discovery…
The $k$-core percolation is a fundamental structural transition in complex networks. Through the analysis of the size jump behaviors of $k$-core in the evolution process of networks, we confirm that $k$-core percolation is continuous phase…
The function of a real network depends not only on the reliability of its own components, but is affected also by the simultaneous operation of other real networks coupled with it. Robustness of systems composed of interdependent network…