Missing Links in Multiple Trade Networks

In this paper we develop a network model of international trade which is able to replicate the concentrated and sparse nature of trade data. Our model extends the preferential attachment (PA) growth model to the case of multiple networks. Countries trade a variety of goods of different complexity. Every country progressively evolves from trading less sophisticated to high-tech goods. The probability to capture more trade opportunities at a given level of complexity and to start trading more complex goods are both proportional to the number of existing trade links. We provide a set of theoretical predictions and simulative results. A calibration exercise shows that our model replicates the same concentration level of world trade as well as the sparsity pattern of the trade matrix. Moreover, we find a lower bound for the share of genuine missing trade links. We also discuss a set of numerical solutions to deal with large multiple networks

Link Prediction via Matrix Completion

Inspired by practical importance of social networks, economic networks, biological networks and so on, studies on large and complex networks have attracted a surge of attentions in the recent years. Link prediction is a fundamental issue to understand the mechanisms by which new links are added to the networks. We introduce the method of robust principal component analysis (robust PCA) into link prediction, and estimate the missing entries of the adjacency matrix. On one hand, our algorithm is based on the sparsity and low rank property of the matrix, on the other hand, it also performs very well when the network is dense. This is because a relatively dense real network is also sparse in comparison to the complete graph. According to extensive experiments on real networks from disparate fields, when the target network is connected and sufficiently dense, whatever it is weighted or unweighted, our method is demonstrated to be very effective and with prediction accuracy being considerably improved comparing with many state-of-the-art algorithms

Unidirectional Quorum-based Cycle Planning for Efficient Resource Utilization and Fault-Tolerance

In this paper, we propose a greedy cycle direction heuristic to improve the generalized $\mathbf{R}$ redundancy quorum cycle technique. When applied using only single cycles rather than the standard paired cycles, the generalized $\mathbf{R}$ redundancy technique has been shown to almost halve the necessary light-trail resources in the network. Our greedy heuristic improves this cycle-based routing technique's fault-tolerance and dependability. For efficiency and distributed control, it is common in distributed systems and algorithms to group nodes into intersecting sets referred to as quorum sets. Optimal communication quorum sets forming optical cycles based on light-trails have been shown to flexibly and efficiently route both point-to-point and multipoint-to-multipoint traffic requests. Commonly cycle routing techniques will use pairs of cycles to achieve both routing and fault-tolerance, which uses substantial resources and creates the potential for underutilization. Instead, we use a single cycle and intentionally utilize $\mathbf{R}$ redundancy within the quorum cycles such that every point-to-point communication pairs occur in at least $\mathbf{R}$ cycles. Without the paired cycles the direction of the quorum cycles becomes critical to the fault tolerance performance. For this we developed a greedy cycle direction heuristic and our single fault network simulations show a reduction of missing pairs by greater than 30%, which translates to significant improvements in fault coverage.Comment: Computer Communication and Networks (ICCCN), 2016 25th International Conference on. arXiv admin note: substantial text overlap with arXiv:1608.05172, arXiv:1608.05168, arXiv:1608.0517

Role models for complex networks

We present a framework for automatically decomposing ("block-modeling") the functional classes of agents within a complex network. These classes are represented by the nodes of an image graph ("block model") depicting the main patterns of connectivity and thus functional roles in the network. Using a first principles approach, we derive a measure for the fit of a network to any given image graph allowing objective hypothesis testing. From the properties of an optimal fit, we derive how to find the best fitting image graph directly from the network and present a criterion to avoid overfitting. The method can handle both two-mode and one-mode data, directed and undirected as well as weighted networks and allows for different types of links to be dealt with simultaneously. It is non-parametric and computationally efficient. The concepts of structural equivalence and modularity are found as special cases of our approach. We apply our method to the world trade network and analyze the roles individual countries play in the global economy