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36
Practical recommendations on crawling online social networks
 SELECTED AREAS IN COMMUNICATIONS, IEEE JOURNAL ON
, 2011
"... Our goal in this paper is to develop a practical framework for obtaining a uniform sample of users in an online social network (OSN) by crawling its social graph. Such a sample allows to estimate any user property and some topological properties as well. To this end, first, we consider and compare ..."
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Cited by 37 (1 self)
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Our goal in this paper is to develop a practical framework for obtaining a uniform sample of users in an online social network (OSN) by crawling its social graph. Such a sample allows to estimate any user property and some topological properties as well. To this end, first, we consider and compare several candidate crawling techniques. Two approaches that can produce approximately uniform samples are the MetropolisHasting random walk (MHRW) and a reweighted random walk (RWRW). Both have pros and cons, which we demonstrate through a comparison to each other as well as to the “ground truth. ” In contrast, using BreadthFirstSearch (BFS) or an unadjusted Random Walk (RW) leads to substantially biased results. Second, and in addition to offline performance assessment, we introduce online formal convergence diagnostics to assess sample quality during the data collection process. We show how these diagnostics can be used to effectively determine when a random walk sample is of adequate size and quality. Third, as a case study, we apply the above methods to Facebook and we collect the first, to the best of our knowledge, representative sample of Facebook users. We make it publicly available and employ it to characterize several key properties of Facebook.
Towards unbiased BFS sampling
 SELECTED AREAS IN COMMUNICATIONS, IEEE JOURNAL ON
, 2011
"... Breadth First Search (BFS) is a widely used approach for sampling large graphs. However, it has been empirically observed that BFS sampling is biased toward highdegree nodes, which may strongly affect the measurement results. In this paper, we quantify and correct the degree bias of BFS. First, we ..."
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Cited by 26 (4 self)
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Breadth First Search (BFS) is a widely used approach for sampling large graphs. However, it has been empirically observed that BFS sampling is biased toward highdegree nodes, which may strongly affect the measurement results. In this paper, we quantify and correct the degree bias of BFS. First, we consider a random graph RG(pk) with an arbitrary degree distribution pk. For this model, we calculate the node degree distribution expected to be observed by BFS as a function of the fraction f of covered nodes. We also show that, for RG(pk), all commonly used graph traversal techniques (BFS, DFS, Forest Fire, Snowball Sampling, RDS) have exactly the same bias. Next, we propose a practical BFSbias correction procedure that takes as input a collected BFS sample together with the fraction f. Our correction technique is exact (i.e., leads to unbiased estimation) for RG(pk). Furthermore, it performs well when applied to a broad range of Internet topologies and to two large BFS samples of Facebook and Orkut networks.
Walking on a Graph with a Magnifying Glass: Stratified Sampling via Weighted Random Walks
 in Proc. ACM SIGMETRICS
, 2011
"... Our objective is to sample the node set of a large unknown graph via crawling, to accurately estimate a given metric of interest. We design a random walk on an appropriately defined weighted graph that achieves high efficiency by preferentially crawling those nodes and edges that convey greater info ..."
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Cited by 23 (7 self)
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Our objective is to sample the node set of a large unknown graph via crawling, to accurately estimate a given metric of interest. We design a random walk on an appropriately defined weighted graph that achieves high efficiency by preferentially crawling those nodes and edges that convey greater information regarding the target metric. Our approach begins by employing the theory of stratification to find optimal node weights, for a given estimation problem, under an independence sampler. While optimal under independence sampling, these weights may be impractical under graph crawling due to constraints arising from the structure of the graph. Therefore, the edge weights for our random walk should be chosen so as to lead to an equilibrium distribution that strikes a balance between approximating the optimal weights under an independence sampler and achieving fast convergence. We propose a heuristic approach (stratified weighted random walk, or SWRW) that achieves this goal, while using only limited information about the graph structure and the node properties. We evaluate our technique in simulation, and experimentally, by collecting a sample of Facebook college users. We show that SWRW requires 1315 times fewer samples than the simple reweighted random walk (RW) to achieve the same estimation accuracy for a range of metrics.
Beyond random walk and metropolishastings samplers: Why you should not backtrack for unbiased graph sampling
, 2012
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Network Sampling: From Static to Streaming Graphs
, 2013
"... Network sampling is integral to the analysis of social, information, and biological networks. Since many realworld networks are massive in size, continuously evolving, and/or distributed in nature, the network structure is often sampled in order to facilitate study. For these reasons, a more thorou ..."
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Cited by 12 (3 self)
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Network sampling is integral to the analysis of social, information, and biological networks. Since many realworld networks are massive in size, continuously evolving, and/or distributed in nature, the network structure is often sampled in order to facilitate study. For these reasons, a more thorough and complete understanding of network sampling is critical to support the field of network science. In this paper, we outline a framework for the general problem of network sampling, by highlighting the different objectives, population and units of interest, and classes of network sampling methods. In addition, we propose a spectrum of computational models for network sampling methods, ranging from the traditionally studied model based on the assumption of a static domain to a more challenging model that is appropriate for streaming domains. We design a family of sampling methods based on the concept of graph induction that generalize across the full spectrum of computational models (from static to streaming) while efficiently preserving many of the topological properties of the input graphs. Furthermore, we demonstrate how traditional static sampling algorithms can be modified for graph streams for each of the three main classes of sampling methods: node, edge, and topologybased sampling. Experimental results indicate that our proposed family of sampling methods more accurately preserve the underlying properties of the graph in both static and streaming domains. Finally, we study the impact of network sampling algorithms on the parameter estimation and performance evaluation of relational classification algorithms.
CoarseGrained Topology Estimation via Graph Sampling
, 2012
"... In many online networks, nodes are partitioned into categories (e.g., countries or universities in OSNs), which naturally defines a weighted category graph i.e., a coarsegrained version of the underlying network. In this paper, we show how to efficiently estimate the category graph from a probabili ..."
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Cited by 10 (4 self)
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In many online networks, nodes are partitioned into categories (e.g., countries or universities in OSNs), which naturally defines a weighted category graph i.e., a coarsegrained version of the underlying network. In this paper, we show how to efficiently estimate the category graph from a probability sample of nodes. We prove consistency of our estimators and evaluate their efficiency via simulation. We also apply our methodology to a sample of Facebook users to obtain a number of category graphs, such as the college friendship graph and the country friendship graph. We share and visualize the resulting data at www.geosocialmap.com.
Online estimating the k central nodes of a network
 In Proc. of the IEEE Network Science Workshop (NSW
, 2011
"... Estimating the most influential nodes in a network is a fundamental problem in network analysis. Influential nodes may be important spreaders of diseases in biological networks, key actors in terrorist networks, or marketing targets in social ..."
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Cited by 6 (4 self)
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Estimating the most influential nodes in a network is a fundamental problem in network analysis. Influential nodes may be important spreaders of diseases in biological networks, key actors in terrorist networks, or marketing targets in social
Quick Detection of Nodes with Large Degrees ⋆
"... Abstract. Our goal is to quickly find top k lists of nodes with the largest degrees in large complex networks. If the adjacency list of the network is known (not often the case in complex networks), a deterministic algorithm to find the top k list of nodes with the largest degrees requires an averag ..."
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Cited by 5 (2 self)
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Abstract. Our goal is to quickly find top k lists of nodes with the largest degrees in large complex networks. If the adjacency list of the network is known (not often the case in complex networks), a deterministic algorithm to find the top k list of nodes with the largest degrees requires an average complexity of O(n), where n is the number of nodes in the network. Even this modest complexity can be very high for large complex networks. We propose to use the random walk based method. We show theoretically and by numerical experiments that for large networks the random walk method finds good quality top lists of nodes with high probability and with computational savings of orders of magnitude. We also propose stopping criteria for the random walk method which requires very little knowledge about the structure of the network. 1
Spaceefficient sampling from social activity streams
 In BigMine
, 2012
"... In order to efficiently study the characteristics of network domains and support development of network systems (e.g. algorithms, protocols that operate on networks), it is often necessary to sample a representative subgraph from a large complex network. Although recent subgraph sampling methods hav ..."
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Cited by 4 (2 self)
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In order to efficiently study the characteristics of network domains and support development of network systems (e.g. algorithms, protocols that operate on networks), it is often necessary to sample a representative subgraph from a large complex network. Although recent subgraph sampling methods have been shown to work well, they focus on sampling from memoryresident graphs and assume that the sampling algorithm can access the entire graph in order to decide which nodes/edges to select. Many largescale network datasets, however, are too large and/or dynamic to be processed using main memory (e.g., email, tweets, wall posts). In this work, we formulate the problem of sampling from large graph streams. We propose a streaming graph sampling algorithm that dynamically maintains a representative sample in a reservoir based setting. We evaluate the efficacy of our proposed methods empirically using several realworld data sets. Across all datasets, we found that our method produce samples that preserve better the original graph distributions. 1.
On the Estimation Accuracy of Degree Distributions from Graph Sampling
"... Abstract — Estimating characteristics of large graphs via sampling is vital in the study of complex networks. In this work, we study the Mean Squared Error (MSE) associated with different sampling methods for the degree distribution. These sampling methods include independent random vertex (RV) and ..."
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Cited by 3 (1 self)
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Abstract — Estimating characteristics of large graphs via sampling is vital in the study of complex networks. In this work, we study the Mean Squared Error (MSE) associated with different sampling methods for the degree distribution. These sampling methods include independent random vertex (RV) and random edge (RE) sampling, and crawling methods such as random walks (RWs) and the widely used MetropolisHastings algorithm for uniformly sampling vertices (MHRWu). We see that the RW MSE is proportional to the RE MSE and inversely proportional to the spectral gap of the RW transition probability matrix. We also determine conditions under which RW is preferable to RV. Finally, we present an approximation of the MHRWu MSE. We evaluate the accuracy of our approximations and bounds through simulations on large real world graphs. I.