A class of networks are those with both positive and negative links. In this manuscript, we studied the interplay between positive and negative ties on mesoscopic level of these networks, i.e., their community structure. A community is considered as a tightly interconnected group of actors; therefore, it does not borrow any assumption from balance theory and merely uses the well-known assumption in the community detection literature. We found that if one detects the communities based on only positive relations (by ignoring the negative ones), the majority of negative relations are already placed between the communities. In other words, negative ties do not have a major role in community formation of signed networks. Moreover, regarding the internal negative ties, we proved that most unbalanced communities are maximally balanced, and hence they cannot be partitioned into k nonempty sub-clusters with higher balancedness (k ≥ 2). Furthermore, we showed that although the mediator triad + + − (hostile-mediator-hostile) is underrepresented, it constitutes a considerable portion of triadic relations among communities. Hence, mediator triads should not be ignored by community detection and clustering algorithms. As a result, if one uses a clustering algorithm that operates merely based on social balance, mesoscopic structure of signed networks significantly remains hidden.

Recommender systems have been accompanied by many applications in both academia and industry. Among different algorithms used to construct a recommender system, collaborative filtering methods have attracted much attention and been used in many commercial applications. Incorporating the time into the recommendation algorithm can greatly enhance its performance. In this paper, we propose a novel time-aware model-based recommendation system. We show that future ratings of a user can be inferred from his/her rating history. We assume that there is cascade of information between the items such that rating an item can lead to other items being rated. There is indeed a hidden network structure among the items and each user tracks a sequence of items in this network. The dependencies between the items are modeled based on statistical diffusion models and the parameters are obtained through maximum-likelihood estimation. We show that under some mild assumptions, the estimation task becomes a convex optimization problem. A major advantage of the proposed method over classical recommender systems is the ability to include novel items in its recommendation lists besides providing accurate recommendations. The proposed model also results in personalized and diverse recommendations. Experimental evaluations show that the model can be trained based on the ratings of a limited number of users. Furthermore, the proposed model outperforms classical recommendation algorithms in terms of both accuracy and novelty.