Related papers: Volumes of Random Alternating Link Diagrams
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Taking up a suggestion of David Gale from 1956, we generate sets of combinatorially isomorphic polytopes by choosing their Gale diagrams at random. We find that in high dimensions, and under suitable assumptions on the growth of the…
Given a set of snapshots from a temporal network we develop, analyze, and experimentally validate a so-called network interpolation scheme. Our method allows us to build a plausible, albeit random, sequence of graphs that transition between…
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Network theory has often disregarded many-body relationships, solely focusing on pairwise interactions: neglecting them, however, can lead to misleading representations of complex systems. Hypergraphs represent a suitable framework for…
We propose a novel statistical model for sparse networks with overlapping community structure. The model is based on representing the graph as an exchangeable point process, and naturally generalizes existing probabilistic models with…
In the last twenty years network science has proven its strength in modelling many real-world interacting systems as generic agents, the nodes, connected by pairwise edges. Yet, in many relevant cases, interactions are not pairwise but…
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Various kinds of spread of influence occur in real world social and virtual networks. These phenomena are formulated by activation processes and irreversible dynamic monopolies in combinatorial graphs representing the topology of the…
Multiplex networks allow us to study a variety of complex systems where nodes connect to each other in multiple ways, for example friend, family, and co-worker relations in social networks. Link prediction is the branch of network analysis…
Hyperbolic space is increasingly used for hierarchical, tree-like, and network-structured data, but likelihood-based density modeling on hyperbolic space remains relatively limited. This paper develops finite mixture modeling with isotropic…
The simulation of traffic flow on networks requires knowledge on the behavior across traffic intersections. For macroscopic models based on hyperbolic conservation laws there exist nowadays many ad-hoc models describing this behavior. Based…
Recent research on network embedding in hyperbolic space have proven successful in several applications. However, nodes in real world networks tend to interact through several distinct channels. Simple aggregation or ignorance of this…
We give a series of combinatorial results that can be obtained from any two collections (both indexed by $\Z\times \N$) of left and right pointing arrows that satisfy some natural relationship. When applied to certain self-interacting…
Recent work on the structure of social networks and the internet has focussed attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distributions that have been widely studied in…
The arrow polynomial is an invariant of framed oriented virtual links that generalizes the virtual Kauffman bracket. In this paper we define the homological arrow polynomial, which generalizes the arrow polynomial to framed oriented virtual…
Principled prediction of when and where links form in complex networks is a fundamental problem. We derive a closed-form non-Markovian expression for next-step connection probabilities that unifies latent hyperbolic geometry with long-range…
We provide precise asymptotic estimates for the number of several classes of labelled cubic planar graphs, and we analyze properties of such random graphs under the uniform distribution. This model was first analyzed by Bodirsky et al.…
This paper focuses on the problem of finding a distribution for an associated entropic vector in the entropy space nearest to a given, possibly non-entropic, target vector for random variables with a constraint on alphabet size. We show the…
We propose a nonparametric approach to link prediction in large-scale dynamic networks. Our model uses graph-based features of pairs of nodes as well as those of their local neighborhoods to predict whether those nodes will be linked at…