Related papers: The theory of percolation on hypergraphs
In order to make more complex number-based strings from topological coding for defending against the intelligent attacks equipped with quantum computing and providing effective protection technology for the age of quantum computing, we will…
The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…
In composite materials composed of soft polymer matrix and stiff, high-aspect-ratio particles, the composite undergoes a transition in mechanical strength when the inclusion phase surpasses a critical density. This phenomenon (rheological…
We describe the critical window for percolation in the universality class of sparse growing random graphs. In our models, vertices arrive sequentially and connect independently to each earlier vertex $v$ with probability proportional to a…
Hypergraph is a general way of representing high-order relations on a set of objects. It is a generalization of graph, in which only pairwise relations can be represented. It finds applications in various domains where relationships of more…
The mathematical analysis of robustness and error-tolerance of complex networks has been in the center of research interest. On the other hand, little work has been done when the attack-tolerance of the vertices or edges are not independent…
Scale-free percolation is a percolation model on $\mathbb{Z}^d$ which can be used to model real-world networks. We prove bounds for the graph distance in the regime where vertices have infinite degrees. We fully characterize transience vs.…
Although well described by mean-field theory in the thermodynamic limit, scaling has long been puzzling for finite systems in high dimensions. This raised questions about the efficacy of the renormalization group and foundational concepts…
Recently the problem of classes of vulnerable vertices (represented by colors) in complex networks has been discussed, where all vertices with the same vulnerability are prone to fail together. Utilizing redundant paths each avoiding one…
Many real-world networks are coupled together to maintain their normal functions. Here we study the robustness of multiplex networks with interdependent and interconnected links under k-core percolation, where a node fails when it connects…
An important class of real-world networks have directed edges, and in addition, some rank ordering on the nodes, for instance the "popularity" of users in online social networks. Yet, nearly all research related to explosive percolation has…
Hypergraphs capture multi-way relationships in data, and they have consequently seen a number of applications in higher-order network analysis, computer vision, geometry processing, and machine learning. In this paper, we develop…
In the analysis of the robustness of multiplex networks, it is commonly assumed that a node is functioning only if its interdependent nodes are simultaneously functioning. According to this model, a multiplex network becomes more and more…
Hypergraphs naturally represent group interactions, which are omnipresent in many domains: collaborations of researchers, co-purchases of items, and joint interactions of proteins, to name a few. In this work, we propose tools for answering…
Geometric and structural constraints greatly restrict the selection of folds adapted by protein backbones, and yet, folded proteins show an astounding diversity in functionality. For structure to have any bearing on function, it is thus…
Percolation theory and the associated conductance networks have provided deep insights into the flow and transport properties of a vast number of heterogeneous materials and media. In practically all cases, however, the conductance of the…
Higher-order interactions provide a nuanced understanding of the relational structure of complex systems beyond traditional pairwise interactions. However, higher-order network analyses also incur more cumbersome interpretations and greater…
Many complex systems involve interactions between more than two agents. Hypergraphs capture these higher-order interactions through hyperedges that may link more than two nodes. We consider the problem of embedding a hypergraph into…
Percolation theory characterizing the robustness of a network has applications ranging from biology, to epidemic spreading, and complex infrastructures. Percolation theory, however, only concern the typical response of a infinite network to…
The acknowledged model for networks of collaborations is the hypergraph model. Nonetheless when it comes to be visualized hypergraphs are transformed into simple graphs. Very often, the transformation is made by clique expansion of the…