Missing and spurious interactions and the reconstruction of complex networks

Abstract

Network analysis is currently used in a myriad of contexts, from identifying potential drug targets to predicting the spread of epidemics and designing vaccination strategies and from finding friends to uncovering criminal activity. Despite the promise of the network approach, the reliability of network data is a source of great concern in all fields where complex networks are studied. Here, we present a general mathematical and computational framework to deal with the problem of data reliability in complex networks. In particular, we are able to reliably identify both missing and spurious interactions in noisy network observations. Remarkably, our approach also enables us to obtain, from those noisy observations, network reconstructions that yield estimates of the true network properties that are more accurate than those provided by the observations themselves. Our approach has the potential to guide experiments, to better characterize network data sets, and to drive new discoveries.data reliability | block model | modularity | node roles | Bayesian inference T he structure of the network of interactions between the units of a system affects the system's dynamics and conveys information about the functional needs of the system, its evolution, and the role of individual units. For these reasons, network analysis has become a cornerstone of fields as diverse as systems biology and sociology (1). Unfortunately, the reliability of network data is often a source of concern. In systems biology, high-throughput technologies hold the promise to uncover the intricate processes within the cell but are also reportedly inaccurate. Protein interaction data provide, arguably, the most blatant example of data inaccuracy: In 2002, a systematic comparison of several highthroughput methods to a reference high-quality data set showed that these methods have accuracies below 20% (2). Additionally, different methods result in networks that have different topological properties (3), and the coverage of real interactomes is very limited: 80% of the interactome of yeast (3) and 99.7% of the human interactome (4, 5) are still unknown.In the social sciences, missing data due to individual nonresponse and dropout (6), informant inaccuracy (7), and sampling biases (8) are also pervasive. Simulation studies have established that these inaccuracies can lead to fundamentally wrong estimates of network properties and to misleading conclusions (8), which is particularly worrisome at a time when social network analysis is being used for finding new friends and partners, singling out key individuals in organizations, and identifying criminal activity.Despite these concerns, the issue of network reliability has only been addressed in a field-by-field basis [for example, to deal with protein-protein interactions (9, 10) or to take into account informant inaccuracy in social networks (7)], and in studies that only address parts of the problem [for example, to detect missing interactions (11)]. Therefore, a general framework to deal with the problem...

Link prediction in complex networks: A survey

“…Notice that, the number of different partitions of N elements grows faster than any finite power of N, and thus even for a small network, to sum over all partitions is not possible in practice. The Metropolis algorithm [94] can be applied to estimate the link reliability [18]. Even though, the whole process is very time consuming and this method can only manage networks with up to a few thousands of nodes.…”

“…The stochastic block model can capture the community structure [22], role-to-role connections [88] and maybe other factors for the establishing of connections, especially when the group membership plays the considerable roles in determining how nodes interact with each other, which usually could not be well described by the simple assortativity coefficient [89,90] or the degree-degree correlations Given a partition M where each node belongs to one group and the connecting probability for two nodes respectively in groups α and β is denoted by Q αβ (Q αα represents the probability that two nodes within group α are connected), then the likelihood of the observed network structure is [18]:…”

“…Denote by Ω the set of all possible partitions, using Bayes' Theorem [93], the reliability of an individual link is [18]:…”

“…In addition, the data in constructing biological and social networks may contain inaccurate information, resulting in spurious links [16,17]. Link prediction algorithms can be applied in identifying these spurious links [18].…”

Credit allocation for research institutes

“…Liang et al [42] found that scientists had referencing misbehavior and behavior of self-copying of references. Therefore, the tolerance of the algorithm against spurious links is an appropriate metric [43]. In this letter, we measure the performance of effectiveness and robustness among the CAM method, Shen's method and (T C) method in rankings by Kendall's Tau, τ and the Jaccard index S when citation links are added or rewired randomly, which is very common in real citation networks [31,44].…”