No Arabic abstract
Over the last two decades, alongside the increased availability of large network datasets, we have witnessed the rapid rise of network science. For many systems, however, the data we have access to is not a direct description of the underlying network. More and more, we see the drive to study networks that have been inferred or reconstructed from non-network data---in particular, using time series data from the nodes in a system to infer likely connections between them. Selecting the most appropriate technique for this task is a challenging problem in network science. Different reconstruction techniques usually have different assumptions, and their performance varies from system to system in the real world. One way around this problem could be to use several different reconstruction techniques and compare the resulting networks. However, network comparison is also not an easy problem, as it is not obvious how best to quantify the differences between two networks, in part because of the diversity of tools for doing so. The netrd Python package seeks to address these two parallel problems in network science by providing, to our knowledge, the most extensive collection of both network reconstruction techniques and network comparison techniques (often referred to as graph distances) in a single library (https://github.com/netsiphd/netrd). In this article, we detail the two main functionalities of the netrd package. Along the way, we describe some of its other useful features. This package builds on commonly used Python packages and is already a widely used resource for network scientists and other multidisciplinary researchers. With ongoing open-source development, we see this as a tool that will continue to be used by all sorts of researchers to come.
Networks can describe the structure of a wide variety of complex systems by specifying which pairs of entities in the system are connected. While such pairwise representations are flexible, they are not necessarily appropriate when the fundamental interactions involve more than two entities at the same time. Pairwise representations nonetheless remain ubiquitous, because higher-order interactions are often not recorded explicitly in network data. Here, we introduce a Bayesian approach to reconstruct latent higher-order interactions from ordinary pairwise network data. Our method is based on the principle of parsimony and only includes higher-order structures when there is sufficient statistical evidence for them. We demonstrate its applicability to a wide range of datasets, both synthetic and empirical.
We study social networks and focus on covert (also known as hidden) networks, such as terrorist or criminal networks. Their structures, memberships and activities are illegal. Thus, data about covert networks is often incomplete and partially incorrect, making interpreting structures and activities of such networks challenging. For legal reasons, real data about active covert networks is inaccessible to researchers. To address these challenges, we introduce here a network generator for synthetic networks that are statistically similar to a real network but void of personal information about its members. The generator uses statistical data about a real or imagined covert organization network. It generates randomized instances of the Stochastic Block model of the network groups but preserves this network organizational structure. The direct use of such anonymized networks is for training on them the research and analytical tools for finding structure and dynamics of covert networks. Since these synthetic networks differ in their sets of edges and communities, they can be used as a new source for network analytics. First, they provide alternative interpretations of the data about the original network. The distribution of probabilities for these alternative interpretations enables new network analytics. The analysts can find community structures which are frequent, therefore stable under perturbations. They may also analyze how the stability changes with the strength of perturbation. For covert networks, the analysts can quantify statistically expected outcomes of interdiction. This kind of analytics applies to all complex network in which the data are incomplete or partially incorrect.
Networks such as social networks, airplane networks, and citation networks are ubiquitous. The adjacency matrix is often adopted to represent a network, which is usually high dimensional and sparse. However, to apply advanced machine learning algorithms to network data, low-dimensional and continuous representations are desired. To achieve this goal, many network embedding methods have been proposed recently. The majority of existing methods facilitate the local information i.e. local connections between nodes, to learn the representations, while completely neglecting global information (or node status), which has been proven to boost numerous network mining tasks such as link prediction and social recommendation. Hence, it also has potential to advance network embedding. In this paper, we study the problem of preserving local and global information for network embedding. In particular, we introduce an approach to capture global information and propose a network embedding framework LOG, which can coherently model {bf LO}cal and {bf G}lobal information. Experimental results demonstrate the ability to preserve global information of the proposed framework. Further experiments are conducted to demonstrate the effectiveness of learned representations of the proposed framework.
Graph models, like other machine learning models, have implicit and explicit biases built-in, which often impact performance in nontrivial ways. The models faithfulness is often measured by comparing the newly generated graph against the source graph using any number or combination of graph properties. Differences in the size or topology of the generated graph therefore indicate a loss in the model. Yet, in many systems, errors encoded in loss functions are subtle and not well understood. In the present work, we introduce the Infinity Mirror test for analyzing the robustness of graph models. This straightforward stress test works by repeatedly fitting a model to its own outputs. A hypothetically perfect graph model would have no deviation from the source graph; however, the models implicit biases and assumptions are exaggerated by the Infinity Mirror test, exposing potential issues that were previously obscured. Through an analysis of thousands of experiments on synthetic and real-world graphs, we show that several conventional graph models degenerate in exciting and informative ways. We believe that the observed degenerative patterns are clues to the future development of better graph models.
We study the problem of optimally investing in nodes of a social network in a competitive setting, wherein two camps aim to drive the average opinion of the population in their own favor. Using a well-established model of opinion dynamics, we formulate the problem as a zero-sum game with its players being the two camps. We derive optimal investment strategies for both camps, and show that a random investment strategy is optimal when the underlying network follows a popular class of weight distributions. We study a broad framework, where we consider various well-motivated settings of the problem, namely, when the influence of a camp on a node is a concave function of its investment on that node, when a camp aims at maximizing competitors investment or deviation from its desired investment, and when one of the camps has uncertain information about the values of the model parameters. We also study a Stackelberg variant of this game under common coupled constraints on the combined investments by the camps and derive their equilibrium strategies, and hence quantify the first-mover advantage. For a quantitative and illustrative study, we conduct simulations on real-world datasets and provide results and insights.