Related papers: Multilateration of Random Networks with Community …
Sampling random nodes is a fundamental algorithmic primitive in the analysis of massive networks, with many modern graph mining algorithms critically relying on it. We consider the task of generating a large collection of random nodes in…
The stochastic block model (SBM) provides a popular framework for modeling community structures in networks. However, more attention has been devoted to problems concerning estimating the latent node labels and the model parameters than the…
We derive rigorous bounds for well-defined community structure in complex networks for a stochastic block model (SBM) benchmark. In particular, we analyze the effect of inter-community "noise" (inter-community edges) on any "community…
We study ensemble-based graph-theoretical methods aiming to approximate the size of the minimum dominating set (MDS) in scale-free networks. We analyze both analytical upper bounds of dominating sets and numerical realizations for…
We study community detection in multiple networks with jointly correlated node attributes and edges. This setting arises naturally in applications such as social platforms, where a shared set of users may exhibit both correlated friendship…
Complex networks often exhibit community structure, with communities corresponding to denser subgraphs in which nodes are closely linked. When modelling systems where interactions extend beyond node pairs to arbitrary numbers of nodes,…
We study a new connection between a technical measure called $\mu$-conductance that arises in the study of Markov chains for sampling convex bodies and the network community profile that characterizes size-resolved properties of clusters…
The smallest set of vertices needed to differentiate or categorize every other vertex in a graph is referred to as the graph's metric dimension. Finding the class of graphs for a particular given metric dimension is an NP-hard problem. This…
Community detection in graphs often relies on ad hoc algorithms with no clear specification about the node partition they define as the best, which leads to uninterpretable communities. Stochastic block models (SBM) offer a framework to…
Dimensionality is one of the most important properties of complex physical systems. However, only recently this concept has been considered in the context of complex networks. In this paper we further develop the previously introduced…
We consider the problem of community detection in the Stochastic Block Model with a finite number $K$ of communities of sizes linearly growing with the network size $n$. This model consists in a random graph such that each pair of vertices…
We investigate a network model based on an infinite regular square lattice embedded in the Euclidean plane where the node connection probability is given by the geometrical distance of nodes. We show that the degree distribution in the…
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…
Multidimensional scaling (MDS) is a popular dimensionality reduction techniques that has been widely used for network visualization and cooperative localization. However, the traditional stress minimization formulation of MDS necessitates…
In this paper, we introduce a new class of stochastic multilayer networks. A stochastic multilayer network is the aggregation of $M$ networks (one per layer) where each is a subgraph of a foundational network $G$. Each layer network is the…
Proximity measures on graphs have a variety of applications in network analysis, including community detection. Previously they have been mainly studied in the context of networks without attributes. If node attributes are taken into…
Community detection in graphs that are generated according to stochastic block models (SBMs) has received much attention lately. In this paper, we focus on the binary symmetric SBM -- in which a graph of $n$ vertices is randomly generated…
The distance of a graph from being triangle-free is a fundamental graph parameter, counting the number of edges that need to be removed from a graph in order for it to become triangle-free. Its corresponding computational problem is the…
This work considers clustering nodes of a largely incomplete graph. Under the problem setting, only a small amount of queries about the edges can be made, but the entire graph is not observable. This problem finds applications in…
Because networks can be used to represent many complex systems, they have attracted considerable attention in physics, computer science, sociology, and many other disciplines. One of the most important areas of network science is the…