The focus of the current research is to identify people of interest in social networks. We are especially interested in studying dark networks, which represent illegal or covert activity. In such networks, people are unlikely to disclose accurate information when queried. We present REDLEARN, an algorithm for sampling dark networks with the goal of identifying as many nodes of interest as possible. We consider two realistic lying scenarios, which describe how individuals in a dark network may attempt to conceal their connections. We test and present our results on several real-world multilayered networks, and show that REDLEARN achieves up to a 340 improvement over the next best strategy.
There are a multitude of sampling techniques for network exploration, including random walks ( @cite_10 , @cite_9 , @cite_5 ), biased random walks ( @cite_3 ), or walks combined with reversible Markov Chains( @cite_15 ), Bayesian methods( @cite_12 ), or standard exhaustive search algorithms like depth-first or breadth-first searches, such as @cite_18 @cite_16 @cite_2 @cite_11 @cite_14 . However, these methods fail in using discovered knowledge, such as node attributes, effectively. Various researchers have considered the problem of sampling for specific goals, such as maximizing the number of nodes observed. For example, Avrachenkov, et al present an algorithm to sample the node with the highest estimated unobserved degree @cite_7 . Hanneke and Xing @cite_17 , and Maiya and Berger-Wolf @cite_4 examine online sampling for centrality measures. Macskassy and Provost develop a guilt-by-association method to identify suspicious individuals in a partially-known network @cite_13 .
@cite_13 @cite_18 @cite_14 @cite_4 @cite_7 @cite_9 @cite_17 @cite_3 @cite_2 @cite_5 @cite_15 @cite_16 @cite_10 @cite_12 @cite_11
180417844 2042359627 1540064387 2117260657
Recently, there has been a great deal of research focusing on the development of sampling algorithms for networks with small-world and or power-law structure. The peerto-peer research community (e.g., [7]) have used sampling to quickly explore and obtain a good representative sample of the network topology, as these networks are hard to explore completely and have significant amounts of churn in their topology. For collecting data from social networks, researchers often use snowball sampling (e.g., [2]) due to the lack of access to the complete graph. have developed Forest Fire Sampling, which uses a hybrid combination of snowball sampling and random-walk sampling to produce samples that match the temporal evolution of the underlying social network [5]. have developed a Metropolis algorithm which samples in a manner designed to match desired properties in the original network [3]. Although there has been a great deal of research focusing on the the development of sampling algorithms, much of this work is based on empirical study and evaluation (i.e., measuring the similarity between sampled and original network properties). There has been some work (e.g., [4, 8, 6]) that has studied the statistical properties of samples of complex networks produced by traditional sampling algorithms such as node sampling, edge sampling and random walks. However, there has been relatively little attention paid to the development of a theoretical foundation for sampling from networks—including a formal framework for sampling, an understanding of various network characteristics and their dependencies, and an analysis of their impact on the accuracy of sampling algorithms. In this paper, we reconsider the foundations of network sampling and attempt to formalize the goals, and process of, sampling, in order to frame future development and analysis of sampling algorithms. Breadth First Search (BFS) and other graph traversal techniques are widely used for measuring large unknown graphs, such as online social networks. It has been empirically observed that incomplete BFS is biased toward high degree nodes. In contrast to more studied sampling techniques, such as random walks, the bias of BFS has not been characterized to date. In this paper, we quantify the degree bias of BFS sampling. In particular, we calculate the node degree distribution expected to be observed by BFS as a function of the fraction of covered nodes, in a random graph RG(p k ) with a given (and arbitrary) degree distribution p k . Furthermore, we also show that, for RG(p k ), all commonly used graph traversal techniques (BFS, DFS, Forest Fire, and Snowball Sampling) lead to the same bias, and we show how to correct for this bias. To give a broader perspective, we compare this class of exploration techniques to random walks that are well-studied and easier to analyze. Next, we study by simulation the effect of graph properties not captured directly by our model. We find that the bias gets amplified in graphs with strong positive assortativity. Finally, we demonstrate the above results by sampling the Facebook social network, and we provide some practical guidelines for graph sampling in practice. Mapping the Internet generally consists in sampling the network from a limited set of sources by using "traceroute"-like probes. This methodology, akin to the merging of different spanning trees to a set of destinations, has been argued to introduce uncontrolled sampling biases that might produce statistical properties of the sampled graph which sharply differ from the original ones. Here we explore these biases and provide a statistical analysis of their origin. We derive a mean-field analytical approximation for the probability of edge and vertex detection that exploits the role of the number of sources and targets and allows us to relate the global topological properties of the underlying network with the statistical accuracy of the sampled graph. In particular we find that the edge and vertex detection probability is depending on the betweenness centrality of each element. This allows us to show that shortest path routed sampling provides a better characterization of underlying graphs with scale-free topology. We complement the analytical discussion with a throughout numerical investigation of simulated mapping strategies in different network models. We show that sampled graphs provide a fair qualitative characterization of the statistical properties of the original networks in a fair range of different strategies and exploration parameters. The numerical study also allows the identification of intervals of the exploration parameters that optimize the fraction of nodes and edges discovered in the sampled graph. This finding might hint the steps toward more efficient mapping strategies. A well known way to find the most central nodes in a network consists of coupling random walk sampling (or one of its variants) with a method to identify the most central nodes in the subgraph induced by the samples. Although it is commonly assumed that degree information is collected during the sampling step, in previous works this information has not been used at the identification step [10], [18]. In this paper, we showed that using degree information at the identification step in a very naive way, namely setting the degree as an alias to other centrality metrics, yields promising results.