Detecting Strong Ties Using Network Motifs

Detecting strong ties among users in social and information networks is a fundamental operation that can improve performance on a multitude of personalization and ranking tasks. Strong-tie edges are often readily obtained from the social network as users often participate in multiple overlapping networks via features such as following and messaging. These networks may vary greatly in size, density and the information they carry. This setting leads to a natural strong tie detection task: given a small set of labeled strong tie edges, how well can one detect unlabeled strong ties in the remainder of the network? This task becomes particularly daunting for the Twitter network due to scant availability of pairwise relationship attribute data, and sparsity of strong tie networks such as phone contacts. Given these challenges, a natural approach is to instead use structural network features for the task, produced by {\em combining} the strong and "weak" edges. In this work, we demonstrate via experiments on Twitter data that using only such structural network features is sufficient for detecting strong ties with high precision. These structural network features are obtained from the presence and frequency of small network motifs on combined strong and weak ties. We observe that using motifs larger than triads alleviate sparsity problems that arise for smaller motifs, both due to increased combinatorial possibilities as well as benefiting strongly from searching beyond the ego network. Empirically, we observe that not all motifs are equally useful, and need to be carefully constructed from the combined edges in order to be effective for strong tie detection. Finally, we reinforce our experimental findings with providing theoretical justification that suggests why incorporating these larger sized motifs as features could lead to increased performance in planted graph models.Comment: To appear in Proceedings of WWW 2017 (Web-science track

Enhanced reconstruction of weighted networks from strengths and degrees

Network topology plays a key role in many phenomena, from the spreading of diseases to that of financial crises. Whenever the whole structure of a network is unknown, one must resort to reconstruction methods that identify the least biased ensemble of networks consistent with the partial information available. A challenging case, frequently encountered due to privacy issues in the analysis of interbank flows and Big Data, is when there is only local (node-specific) aggregate information available. For binary networks, the relevant ensemble is one where the degree (number of links) of each node is constrained to its observed value. However, for weighted networks the problem is much more complicated. While the naive approach prescribes to constrain the strengths (total link weights) of all nodes, recent counter-intuitive results suggest that in weighted networks the degrees are often more informative than the strengths. This implies that the reconstruction of weighted networks would be significantly enhanced by the specification of both strengths and degrees, a computationally hard and bias-prone procedure. Here we solve this problem by introducing an analytical and unbiased maximum-entropy method that works in the shortest possible time and does not require the explicit generation of reconstructed samples. We consider several real-world examples and show that, while the strengths alone give poor results, the additional knowledge of the degrees yields accurately reconstructed networks. Information-theoretic criteria rigorously confirm that the degree sequence, as soon as it is non-trivial, is irreducible to the strength sequence. Our results have strong implications for the analysis of motifs and communities and whenever the reconstructed ensemble is required as a null model to detect higher-order patterns

Link-Prediction Enhanced Consensus Clustering for Complex Networks

Many real networks that are inferred or collected from data are incomplete due to missing edges. Missing edges can be inherent to the dataset (Facebook friend links will never be complete) or the result of sampling (one may only have access to a portion of the data). The consequence is that downstream analyses that consume the network will often yield less accurate results than if the edges were complete. Community detection algorithms, in particular, often suffer when critical intra-community edges are missing. We propose a novel consensus clustering algorithm to enhance community detection on incomplete networks. Our framework utilizes existing community detection algorithms that process networks imputed by our link prediction based algorithm. The framework then merges their multiple outputs into a final consensus output. On average our method boosts performance of existing algorithms by 7% on artificial data and 17% on ego networks collected from Facebook