Related papers: A threshold for cutoff in two-community random gra…
Statistical significance of network clustering has been an unresolved problem since it was observed that community detection algorithms produce false positives even in random graphs. After a phase transition between undetectable and…
With the increase of the elderly and disabled in the world, the characteristics of pedestrian flow mixed with wheelchair users has being paid more and more attention. In this study, experiments in funnel-shaped bottlenecks were performed to…
Unsupervised node clustering (or community detection) is a classical graph learning task. In this paper, we study algorithms, which exploit the geometry of the graph to identify densely connected substructures, which form clusters or…
The analysis of multilayer networks is among the most active areas of network science, and there are now several methods to detect dense "communities" of nodes in multilayer networks. One way to define a community is as a set of nodes that…
The betweenness centrality of graphs using random walk paths instead of geodesics is studied. A scaling collapse with no adjustable parameters is obtained as the graph size $N$ is varied; the scaling curve depends on the graph model. A…
Communities are subsets of a network that are densely connected inside and share only few connections to the rest of the network. The aim of this research is the development and evaluation of an efficient algorithm for detection of…
Random walks including non-nearest-neighbor jumps appear in many real situations such as the diffusion of adatoms and have found numerous applications including PageRank search algorithm, however, related theoretical results are much less…
Discovered in the context of card shuffling by Aldous, Diaconis and Shahshahani, the cutoff phenomenon has since then been established in a variety of Markov chains. However, proving cutoff remains a delicate affair, which requires a…
In this paper, we study the scaling limit of a class of random walks which behave like simple random walks outside of a bounded region around the origin and which are subject to a partial reflection near the origin. If the probability of…
The mixing time of a graph is an important metric, which is not only useful in analyzing connectivity and expansion properties of the network, but also serves as a key parameter in designing efficient algorithms. We present an efficient…
The study of time-varying (dynamic) networks (graphs) is of fundamental importance for computer network analytics. Several methods have been proposed to detect the effect of significant structural changes in a time series of graphs. The…
We show that by restricting the degrees of the vertices of a graph to an arbitrary set \( \Delta \), the threshold point $ \alpha(\Delta) $ of the phase transition for a random graph with $ n $ vertices and $ m = \alpha(\Delta) n $ edges…
Random geometric graphs result from taking $n$ uniformly distributed points in the unit cube, $[0,1]^d$, and connecting two points if their Euclidean distance is at most $r$, for some prescribed $r$. We show that monotone properties for…
Interaction between vehicles and pedestrians is seen in many areas such as crosswalks and intersections. In this paper, we study a totally asymmetric simple exclusion process with a bottleneck at a boundary caused by an interaction. Due to…
A recently proposed graph-theoretic metric, the influence gap, has shown to be a reliable predictor of the effect of social influence in two-party elections, albeit only tested on regular and scale-free graphs. Here, we investigate whether…
The random-cluster model has been widely studied as a unifying framework for random graphs, spin systems and electrical networks, but its dynamics have so far largely resisted analysis. In this paper we analyze the Glauber dynamics of the…
Random walks on expander graphs were thoroughly studied, with the important motivation that, under some natural conditions, these walks mix quickly and provide an efficient method of sampling the vertices of a graph. Alon, Benjamini,…
We are interested in recovering information on a stochastic block model from the subgraph discovered by an exploring random walk. Stochastic block models correspond to populations structured into a finite number of types, where two…
Community detection or clustering is a crucial task for understanding the structure of complex systems. In some networks, nodes are permitted to be linked by either "positive" or "negative" edges; such networks are called signed networks.…
Consider a continuous time random walk in $\mathbb{Z}$ with independent and exponentially distributed jumps $\pm1$. The model in this paper consists in an infinite number of such random walks starting from the complement of…