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Networks are a fundamental tool for understanding and modeling complex systems in physics, biology, neuroscience, engineering, and social science. Many networks are known to exhibit rich, lower-order connectivity patterns that can be…
We analyze dynamic random network models where younger vertices connect to older ones with probabilities proportional to their degrees as well as a propensity kernel governed by their attribute types. Using stochastic approximation…
Modern network analysis often involves multi-layer network data in which the nodes are aligned, and the edges on each layer represent one of the multiple relations among the nodes. Current literature on multi-layer network data is mostly…
Many patterns have been uncovered in complex systems through the application of concepts and methodologies of complex networks. Unfortunately, the validity and accuracy of the unveiled patterns are strongly dependent on the amount of…
Modularity is designed to measure the strength of division of a network into clusters (known also as communities). Networks with high modularity have dense connections between the vertices within clusters but sparse connections between…
Spatially constrained planar networks are frequently encountered in real-life systems. In this paper, based on a space-filling disk packing we propose a minimal model for spatial maximal planar networks, which is similar to but different…
We study a recently introduced class of scale-free networks showing a high clustering coefficient and non-trivial connectivity correlations. We find that the connectivity probability distribution strongly depends on the fine details of the…
While the majority of approaches to the characterization of complex networks has relied on measurements considering only the immediate neighborhood of each network node, valuable information about the network topological properties can be…
The paper tackles the problem of clustering multiple networks, directed or not, that do not share the same set of vertices, into groups of networks with similar topology. A statistical model-based approach based on a finite mixture of…
Distributed processing over networks relies on in-network processing and cooperation among neighboring agents. Cooperation is beneficial when agents share a common objective. However, in many applications agents may belong to different…
The idea underlying the modal formulation of density-based clustering is to associate groups with the regions around the modes of the probability density function underlying the data. This correspondence between clusters and dense regions…
Usual formulations of the clustering coefficient can be shown to be insufficient in the task of describing the local topology of very simple networks. Motivated by this, we review some alternatives in order to present an extension, the…
Probabilistic clustering models (or equivalently, mixture models) are basic building blocks in countless statistical models and involve latent random variables over discrete spaces. For these models, posterior inference methods can be…
Meso-scale structures are network features where nodes with similar properties are grouped together instead of being treated individually. In this work, we provide formal and mathematical definitions of three such structures: assortative…
With complex networks emerging as an effective tool to tackle multidisciplinary problems, models of network generation have gained an importance of their own. These models allow us to extensively analyze the data obtained from real-world…
In this paper, we investigate the effect of local structures on network processes. We investigate a random graph model that incorporates local clique structures to deviate from the locally tree-like behavior of most standard random graph…
The social networks that infectious diseases spread along are typically clustered. Because of the close relation between percolation and epidemic spread, the behavior of percolation in such networks gives insight into infectious disease…
Core-periphery is a key feature of large-scale networks underlying a wide range of social, biological, and transportation phenomena. Despite its prevalence in empirical data, it is unclear whether this property is a consequence of more…
We discuss three related models of scale-free networks with the same degree distribution but different correlation properties. Starting from the Barabasi-Albert construction based on growth and preferential attachment we discuss two other…
We investigate the presence of triangles in a class of correlated random graphs in which hidden variables determine the pairwise connections between vertices. The class rules out self-loops and multiple edges and allows for negative degree…