Related papers: Random graph ensembles with many short loops

We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short range correlations in the level spacings of the…

We develop a new sampling method to estimate eigenvector centrality on incomplete networks. Our goal is to estimate this global centrality measure having at disposal a limited amount of data. This is the case in many real-world scenarios…

Learning properties of large graphs from samples has been an important problem in statistical network analysis since the early work of Goodman \cite{Goodman1949} and Frank \cite{Frank1978}. We revisit a problem formulated by Frank…

Small-world networks provide an interesting framework for studying the interplay between regular and random graphs, where links are located in a regular and random way, respectively. On one hand, the random links make the model to obey some…

Characterization of real-world complex systems increasingly involves the study of their topological structure using graph theory. Among global network properties, small-world property, consisting in existence of relatively short paths…

Network models have been widely used to study diverse systems and analyze their dynamic behaviors. Given the structural variability of networks, an intriguing question arises: Can we infer the type of system represented by a network based…

We analyze complex networks under random matrix theory framework. Particularly, we show that $\Delta_3$ statistic, which gives information about the long range correlations among eigenvalues, provides a qualitative measure of randomness in…

We propose a family of lagged random walk sampling methods in simple undirected graphs, where transition to the next state (i.e. node) depends on both the current and previous states -- hence, lagged. The existing random walk sampling…

We consider the problem of estimating the topology of multiple networks from nodal observations, where these networks are assumed to be drawn from the same (unknown) random graph model. We adopt a graphon as our random graph model, which is…

We present an analytical approach for describing spectrally constrained maximum entropy ensembles of finitely connected regular loopy graphs, valid in the regime of weak loop-loop interactions. We derive an expression for the leading two…

Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely…

This paper revisits the classical concept of network modularity and its spectral relaxations used throughout graph data analysis. We formulate and study several modularity statistic variants for which we establish asymptotic distributional…

The problem of defining a statistical ensemble of random graphs with an arbitrary connectivity distribution is discussed. Introducing such an ensemble is a step towards uderstanding the geometry of wide classes of graphs independently of…

A graph homomorphism is a map between two graphs that preserves adjacency relations. We consider the problem of sampling a random graph homomorphism from a graph into a large network. We propose two complementary MCMC algorithms for…

Large real-world graphs tend to be sparse, but they often contain many densely connected subgraphs and exhibit high clustering coefficients. While recent random graph models can capture this sparsity, they ignore the local density, or vice…

Network analysis is currently used in a myriad of contexts: from identifying potential drug targets to predicting the spread of epidemics and designing vaccination strategies, and from finding friends to uncovering criminal activity.…

We introduce recursive corona graphs as a model of small-world networks. We investigate analytically the critical characteristics of the model, including order and size, degree distribution, average path length, clustering coefficient, and…

Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…

Random walk-based sampling methods are gaining popularity and importance in characterizing large networks. While powerful, they suffer from the slow mixing problem when the graph is loosely connected, which results in poor estimation…

Recovering the random graph model from an observed collection of networks is known to present significant challenges in the setting, where the networks do not share a common node set and have different sizes. More specifically, the goal is…