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Landing probabilities (LP) of random walks (RW) over graphs encode rich information regarding graph topology. Generalized PageRanks (GPR), which represent weighted sums of LPs of RWs, utilize the discriminative power of LP features to…
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…
Partially-observed network data collected by link-tracing based sampling methods is often being studied to obtain the characteristics of a large complex network. However, little attention has been paid to sampling from directed networks…
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…
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…
Given a graph $G$, a source node $s$ and a target node $t$, the personalized PageRank (PPR) of $t$ with respect to $s$ is the probability that a random walk starting from $s$ terminates at $t$. An important variant of the PPR query is…
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…
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.…
We study the behavior of network diffusions based on the PageRank random walk from a set of seed nodes. These diffusions are known to reveal small, localized clusters (or communities) and also large macro-scale clusters by varying a…
PageRank (PR) is a fundamental tool for assessing the relative importance of the nodes in a network. In this paper, we propose a measure, weighted PageRank (WPR), extended from the classical PR for weighted, directed networks with possible…
In theory, a major advantage to the big data approach in studying online communities is that it should be possible to collect a representative random sample from a broadly defined population. However, in practice, data collection processes…
Graph Neural Networks (GNNs) have achieved great successes in many learning tasks performed on graph structures. Nonetheless, to propagate information GNNs rely on a message passing scheme which can become prohibitively expensive when…
Personalized PageRank (PPR) is a popular node proximity metric in graph mining and network research. Given a graph G=(V,E) and a source node $s \in V$, a single-source PPR (SSPPR) query asks for the PPR value $\vpi(u)$ with respect to s,…
Given an undirected graph $G=(V, E)$, the Personalized PageRank (PPR) of $t\in V$ with respect to $s\in V$, denoted $\pi(s,t)$, is the probability that an $\alpha$-discounted random walk starting at $s$ terminates at $t$. We study the time…
We analyze dynamic random network models where younger vertices connect to older ones with probabilities proportional to their degrees as well as a propensity kernel governed by their attribute types. Using stochastic approximation…
This work proposes a novel framework based on nested evolving set processes to accelerate Personalized PageRank (PPR) computation. At each stage of the process, we employ a localized inexact proximal point iteration to solve a simplified…
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…
We propose and analyze two algorithms for maintaining approximate Personalized PageRank (PPR) vectors on a dynamic graph, where edges are added or deleted. Our algorithms are natural dynamic versions of two known local variations of power…
Neural message passing algorithms for semi-supervised classification on graphs have recently achieved great success. However, for classifying a node these methods only consider nodes that are a few propagation steps away and the size of…
We present new results on community recovery based on the PageRank Nibble algorithm on a sparse directed stochastic block model (dSBM). Our results are based on a characterization of the local weak limit of the dSBM and the limiting…