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We report on the use of novel mathematical methods in hypergraph analytics over a large quantity of DNS data. Hypergraphs generalize graphs, as used in network science, to better model complex multiway relations in cyber data. Specifically, ...

Recently, non-Euclidean spaces became popular for embedding structured data. However, determining suitable geometry and, in particular, curvature for a given dataset is still an open problem. In this paper, we define a notion of global graph ...

This work introduces the problem of social influence diffusion in complex networks, where vertices are linked not only through simple pairwise relationships to other nodes but with groups of nodes of arbitrary size. A challenging problem that ...

Graph embedding is a transformation of vertices of a graph into a set of vectors. A good embedding should capture the graph topology, vertex-to-vertex relationship, and other relevant information about the graph, its subgraphs, and vertices. If ...

A probabilistic generative network model with n nodes and m overlapping layers is obtained as a superposition of m mutually independent Bernoulli random graphs of varying size and strength. When n and m are large and of the same order of magnitude,...

It is well known that the global clustering coefficient of a standard preferential attachment random graph vanishes as the number of vertices tends to . We evaluate the global clustering coefficient of the preferred attachment affiliation network [...

Weight-dependent random connection graphs are a class of local network models that combine scale-free degree distribution, small-world properties and clustering. In this paper we discuss recurrence or transience of these graphs, features that are ...

We introduce a new, deterministic directed graph model for social networks, based on the transitivity of triads. In the Iterated Local Directed Transitivity (ILDT) model, new nodes are born over discrete time-steps and inherit the link structure ...

We establish the rapid mixing property of a binomial random intersection graph introduced in [11, 17]. For this purpose we show that the conductance is bounded away from zero by a positive constant. We consider the range of parameters n, m, p ...

We introduce the Iterated Global model as a deterministic graph process that simulates several properties of complex networks. In this model, for every set S of nodes of a prescribed cardinality, we add a new node that is adjacent to every node in ...

The World-Wide-Web is a complex system naturally represented by a directed network of documents (nodes) connected through hyperlinks (edges). In this work, we focus on one of the most relevant topological properties that characterize the network, ...

Using a game-theoretic framework, we characterize the community structure that emerges in a social (information) network. Our analysis generalizes the results in [1, 2] that were obtained for the case of a continuous population model for the ...