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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…

Local graph clustering methods aim to detect small clusters in very large graphs without the need to process the whole graph. They are fundamental and scalable tools for a wide range of tasks such as local community detection, node ranking…

Random K-out graphs are used in several applications including modeling by sensor networks secured by the random pairwise key predistribution scheme, and payment channel networks. The random K-out graph with $n$ nodes is constructed as…

Graph kernels are widely used for measuring the similarity between graphs. Many existing graph kernels, which focus on local patterns within graphs rather than their global properties, suffer from significant structure information loss when…

We study spatial embeddings of random graphs in which nodes are randomly distributed in geographical space. We let the edge probability between any two nodes to be dependent on the spatial distance between them and demonstrate that this…

Random spatial networks-that is, graphs whose connectivity is governed by geometric proximity-have emerged as fundamental models for systems constrained by an underlying spatial structure. A prototypical example is the random geometric…

There has been much recent interest in random graphs sampled uniformly from the n-vertex graphs in a suitable minor-closed class, such as the class of all planar graphs. Here we use combinatorial and probabilistic methods to investigate a…

We propose and study a hierarchical algorithm to generate graphs having a predetermined distribution of cliques, the fully connected subgraphs. The construction mechanism may be either random or incorporate preferential attachment. We…

The clustering attachment model introduced in the paper Bagrow and Brockmann (2013) may be used as an evolution tool of random networks. We propose a new clustering attachment model which can be considered as the limit of the former…

Although the analysis of loops is not so much because of the complications, it has already been found that heuristically enhancing loops decreases the variance of degree distributions for improving the robustness of connectivity. While many…

We propose a Markov chain simulation method to generate simple connected random graphs with a specified degree sequence and level of clustering. The networks generated by our algorithm are random in all other respects and can thus serve as…

This article explores and analyzes the unsupervised clustering of large partially observed graphs. We propose a scalable and provable randomized framework for clustering graphs generated from the stochastic block model. The clustering is…

Graphs and networks are used to model interactions in a variety of contexts. There is a growing need to quickly assess the characteristics of a graph in order to understand its underlying structure. Some of the most useful metrics are…

A random network model which allows for tunable, quite general forms of clustering, degree correlation and degree distribution is defined. The model is an extension of the configuration model, in which stubs (half-edges) are paired to form…

We consider a class of growing random graphs obtained by creating vertices sequentially one by one: at each step, we choose uniformly the neighbours of the newly created vertex; its degree is a random variable with a fixed but arbitrary…

I start by reviewing some basic properties of random graphs. I then consider the role of random walks in complex networks and show how they may be used to explain why so many long tailed distributions are found in real data sets. The key…

Many machine learning algorithms used for dimensional reduction and manifold learning leverage on the computation of the nearest neighbours to each point of a dataset to perform their tasks. These proximity relations define a so-called…

The clustering property of complex networks indicates the abundance of small dense subgraphs in otherwise sparse networks. For a community-affiliation network defined by a superposition of Bernoulli random graphs, which has a nonvanishing…

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…

Soft Random Geometric Graphs (SRGGs) have been widely applied to various models including those of wireless sensor, communication, social and neural networks. SRGGs are constructed by randomly placing nodes in some space and making pairwise…