Related papers: Approximating Sparse Graphs: The Random Overlappin…
A new efficient algorithm is presented for finding all simple cycles that satisfy a length constraint in a directed graph. When the number of vertices is non-trivial, most cycle-finding problems are of practical interest for sparse graphs…
Inference of community structure in probabilistic graphical models may not be consistent with fairness constraints when nodes have demographic attributes. Certain demographics may be over-represented in some detected communities and…
The spectral density of random graphs with topological constraints is analysed using the replica method. We consider graph ensembles featuring generalised degree-degree correlations, as well as those with a community structure. In each case…
We introduce and develop a theory of limits for sequences of sparse graphs based on $L^p$ graphons, which generalizes both the existing $L^\infty$ theory of dense graph limits and its extension by Bollob\'as and Riordan to sparse graphs…
We propose that hypergraphs can be used to model social networks with overlapping communities. The nodes of the hypergraphs represent the communities. The hyperlinks of the hypergraphs denote the individuals who may participate in multiple…
Degree distribution, or equivalently called degree sequence, has been commonly used to be one of most significant measures for studying a large number of complex networks with which some well-known results have been obtained. By contrast,…
Preferential attachment graphs are random graphs designed to mimic properties of typical real world networks. They are constructed by a random process that iteratively adds vertices and attaches them preferentially to vertices that already…
Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. We consider a relaxed version of this problem in the setting of local algorithms. The relaxation is that the constructed subgraph is a sparse spanning…
The stochastic block model is a canonical random graph model for clustering and community detection on network-structured data. Decades of extensive study on the problem have established many profound results, among which the phase…
Uniform sampling of simple graphs having a given degree sequence is a known problem with exponential complexity in the square of the mean degree. For undirected graphs, randomised approximation algorithms have nonetheless been shown to…
We consider random walks in the form of nearest-neighbor hopping on Erdos-Renyi random graphs of finite fixed mean degree c as the number of vertices N tends to infinity. In this regime, using statistical field theory methods, we develop an…
Dense subgraphs of sparse graphs (communities), which appear in most real-world complex networks, play an important role in many contexts. Computing them however is generally expensive. We propose here a measure of similarities between…
In this paper we consider the Erd\H{o}s-R\'enyi random graph in the sparse regime in the limit as the number of vertices $n$ tends to infinity. We are interested in what this graph looks like when it contains many triangles, in two…
Graphlets are induced subgraph patterns that are crucial to the understanding of the structure and function of a large network. A lot of efforts have been devoted to calculating graphlet statistics where random walk based approaches are…
Let $\mathbb{G}^{D}$ be the set of graphs $G(V,\, E)$ with $\left|V\right|=n$, and the degree sequence equal to $D=(d_{1},\, d_{2},\,\dots,\, d_{n})$. In addition, for $\frac{1}{2}<a<1$, we define the set of graphs with an almost given…
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…
The stochastic block model is widely used to generate graphs with a community structure, but no simple alternative currently exists for hypergraphs, in which more than two nodes can be connected together through a hyperedge. We discuss here…
We consider the task of topology discovery of sparse random graphs using end-to-end random measurements (e.g., delay) between a subset of nodes, referred to as the participants. The rest of the nodes are hidden, and do not provide any…
The problem of computing the vertex expansion of a graph is an NP-hard problem. The current best worst-case approximation guarantees for computing the vertex expansion of a graph are a $O(\sqrt{\log n})$-approximation algorithm due to…
The sparse representation classifier (SRC) is shown to work well for image recognition problems that satisfy a subspace assumption. In this paper we propose a new implementation of SRC via screening, establish its equivalence to the…