Related papers: Thresholds and Fluctuations of Submultiplexes in R…
We consider classes of pseudo-random graphs on $n$ vertices for which the degree of every vertex and the co-degree between every pair of vertices are in the intervals $(np - Cn^\delta,np+Cn^\delta)$ and $(np^2- C n^\delta, np^2 +C…
This paper introduces a nonparametric framework for the setting where multiple networks are observed on the same set of nodes, also known as multiplex networks. Our objective is to provide a simple parameterization which explicitly captures…
Multiplex networks are collections of networks with identical nodes but distinct layers of edges. They are genuine representations for a large variety of real systems whose elements interact in multiple fashions or flavors. However,…
The characterization of various properties of real-world systems requires the knowledge of the underlying network of connections among the system's components. Unfortunately, in many situations the complete topology of this network is…
The maximum likelihood threshold (MLT) of a graph $G$ is the minimum number of samples to almost surely guarantee existence of the maximum likelihood estimate in the corresponding Gaussian graphical model. We give a new characterization of…
In random graph models, the degree distribution of an individual node should be distinguished from the (empirical) degree distribution of the graph that records the fractions of nodes with given degree. We introduce a general framework to…
Quite often real-world networks can be thought of as being symmetric, in the abstract sense that vertices can be found to have similar or equivalent structural roles. However, traditional measures of symmetry in graphs are based on their…
We consider a statistical model for the problem of finding subgraphs with specified topology in an otherwise random graph. This task plays an important role in the analysis of social and biological networks. In these types of networks,…
Multiplex networks are a powerful framework for representing systems with multiple types of interactions among a common set of entities. Understanding their structure requires statistical tools capturing higher-order cross-layer…
Many real-world networks describe systems in which interactions decay with the distance between nodes. Examples include systems constrained in real space such as transportation and communication networks, as well as systems constrained in…
In previous papers, threshold probabilities for the properties of a random distance graph to contain strictly balanced graphs were found. We extend this result to arbitrary graphs and prove that the number of copies of a strictly balanced…
In their seminal paper introducing the theory of random graphs, Erd\H{o}s and R\'{e}nyi considered the evolution of the structure of a random subgraph of $K_n$ as the density increases from $0$ to $1$, identifying two key points in this…
Graph symmetries intervene in diverse applications, from enumeration, to graph structure compression, to the discovery of graph dynamics (e.g., node arrival order inference). Whereas Erd\H{o}s-R\'enyi graphs are typically asymmetric, real…
We consider a random geometric hypergraph model based on an underlying bipartite graph. Nodes and hyperedges are sampled uniformly in a domain, and a node is assigned to those hyperedges that lie with a certain radius. From a modelling…
There is growing interest in multiplex networks where individual nodes take part in several layers of networks simultaneously. This is the case for example in social networks where each individual node has different kind of social ties or…
The $\boldsymbol{\beta}$-model for random graphs is commonly used for representing pairwise interactions in a network with degree heterogeneity. Going beyond pairwise interactions, Stasi et al. (2014) introduced the hypergraph…
Misinformation is pervasive in natural, biological, social, and engineered systems, yet its quantitative characterization remains challenging. We develop a general mathematical framework for quantifying information distortion in distributed…
Network motifs are characteristic patterns which occur in the networks essentially more frequently than the other patterns. For five motifs found in S. Itzkovitz, U. Alon, Phys. Rev.~E, 2005, 71, 026117-1, hierarchical random graphs are…
Graph-theoretic tools and techniques have seen wide use in the multi-agent systems literature, and the unpredictable nature of some multi-agent communications has been successfully modeled using random communication graphs. Across both…
Conventionally, pairwise relationships between nodes are considered to be the fundamental building blocks of complex networks. However, over the last decade the overabundance of certain sub-network patterns, so called motifs, has attracted…