Related papers: Personalized PageRank Estimation in Undirected Gra…
PageRank has numerous applications in information retrieval, reputation systems, machine learning, and graph partitioning.In this paper, we study PageRank in undirected random graphs with expansion property. The Chung-Lu random graph…
Most methods for Personalized PageRank (PPR) precompute and store all accurate PPR vectors, and at query time, return the ones of interest directly. However, the storage and computation of all accurate PPR vectors can be prohibitive for…
Query evaluation over probabilistic databases is notoriously intractable -- not only in combined complexity, but often in data complexity as well. This motivates the study of approximation algorithms, and particularly of combined FPRASes,…
Random planar graphs have been the subject of much recent work. Many basic properties of the standard uniform random planar graph P_{n}, by which we mean a graph chosen uniformly at random from the set of all planar graphs with vertex set…
Given an input graph G and a node v in G, homogeneous network embedding (HNE) maps the graph structure in the vicinity of v to a compact, fixed-dimensional feature vector. This paper focuses on HNE for massive graphs, e.g., with billions of…
There has been a rising interest in graph neural networks (GNNs) for representation learning over the past few years. GNNs provide a general and efficient framework to learn from graph-structured data. However, GNNs typically only use the…
In this paper new results on personalized PageRank are shown. We consider directed graphs that may contain dangling nodes. The main result presented gives an analytical characterization of all the possible values of the personalized…
Consider the setting of \emph{randomly weighted graphs}, namely, graphs whose edge weights are chosen independently according to probability distributions with finite support over the non-negative reals. Under this setting, properties of…
We consider the distributed optimization problem for the sum of convex functions where the underlying communications network connecting agents at each time is drawn at random from a collection of directed graphs. Building on an earlier work…
Node embedding learns low-dimensional vectors for nodes in the graph. Recent state-of-the-art embedding approaches take Personalized PageRank (PPR) as the proximity measure and factorize the PPR matrix or its adaptation to generate…
An algorithm observes the trajectories of random walks over an unknown graph $G$, starting from the same vertex $x$, as well as the degrees along the trajectories. For all finite connected graphs, one can estimate the number of edges $m$ up…
We analyze the distribution of PageRank on a directed configuration model and show that as the size of the graph grows to infinity it can be closely approximated by the PageRank of the root node of an appropriately constructed tree. This…
Popular graph neural networks are shallow models, despite the success of very deep architectures in other application domains of deep learning. This reduces the modeling capacity and leaves models unable to capture long-range relationships.…
For a directed graph, the Pagerank algorithm emulates a random walker on the graph that occasionally "jumps" to a random vertex based on a jumping parameter $\alpha$. Upon completion, the algorithm generates a stochastic vector whose…
Based on observations in the web-graph, the power-law hypothesis states that PageRank has a power-law distribution with the same exponent as the in-degree. While this hypothesis has been analytically verified for many random graph models,…
We study a general class of PageRank optimization problems which consist in finding an optimal outlink strategy for a web site subject to design constraints. We consider both a continuous problem, in which one can choose the intensity of a…
We prove new results on lazy random walks on finite graphs. To start, we obtain new estimates on return probabilities $P^t(x,x)$ and the maximum expected hitting time $t_{\rm hit}$, both in terms of the relaxation time. We also prove a…
An uncertain graph $\mathcal{G} = (V, E, p : E \rightarrow (0,1])$ can be viewed as a probability space whose outcomes (referred to as \emph{possible worlds}) are subgraphs of $\mathcal{G}$ where any edge $e\in E$ occurs with probability…
In this paper some results about the controllability of spectral centrality in a complex network are presented. In particular, the inverse problem of designing an unweigthed graph with a prescribed centrality is considered, by showing that…
Orienteering is the following optimization problem: given an edge-weighted graph (directed or undirected), two nodes s,t and a time limit T, find an s-t walk of total length at most T that maximizes the number of distinct nodes visited by…