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Wikipedia is a widely used tool people use to gather knowledge about the world, causing it to have a vast impact on the way individuals perceive the reality they live in. It is then of paramount importance that the picture of the world Wikipedia provides is accurate. We cannot afford such an important tool to eschew inclusiveness or a fair representation of reality: an inaccurate picture of the world in such a tool can be used to claim unjust and unfair positions — such as that women are inferior to men — as if they were facts, because they are enshrined on an encyclopedia. In this paper, we study issues of fair gender representations for people in history noted by multiple language editions of Wikipedia: are women underrepresented on Wikipedia? We do so via a combination of natural language processing and network science. Our results indicate that there is indeed a higher bar for women to have their own biographical page on Wikipedia: women are only included when they have more significant connections than men to the rest of the network. There are visible effects of the initiatives Wikipedia is taking to fix this issue, showing that the gap is narrowing, which validates our interpretation of the data. [ABSTRACT FROM AUTHOR]

Estimating the distance covered by a spreading event on a network can lead to a better understanding of epidemics, economic growth, and human behavior. There are many methods solving this problem--which has been called Node Vector Distance (NVD)--for single layer networks. However, many phenomena are better represented by multilayer networks: networks in which nodes can connect in qualitatively different ways. In this article, we extend the literature by proposing an algorithm solving NVD for multilayer networks. We do so by adapting the Mahalanobis distance, incorporating the graph's topology via the pseudoinverse of its Laplacian. Since this is a proper generalization of the Euclidean distance in a complex space defined by the topology of the graph, and that it works on multilayer networks, we call our measure the Multi Layer Generalized Euclidean (MLGE). In our experiments, we show that MLGE is intuitive, theoretically simpler than the alternatives, performs well in recovering infection parameters, and it is useful in specific case studies. MLGE requires solving a special case of the effective resistance on the graph, which has a high time complexity. However, this needs to be done only once per network. In the experiments, we show that MLGE can cache its most computationally heavy parts, allowing it to solve hundreds of NVD problems on the same network with little to no additional runtime. MLGE is provided as a free open source tool, along with the data and the code necessary to replicate our results. [ABSTRACT FROM AUTHOR]

Estimating the trustworthiness of a set of actors when all the available information is provided by the actors themselves is a hard problem. When two actors have conflicting reports about each other, how do we establish which of the two (if any) deserves our trust? In this paper, we model this scenario as a network problem: actors are nodes in a network and their reports about each other are the edges of the network. To estimate their trustworthiness levels, we develop an iterative framework which looks at all the reports about each connected actor pair to define its trustworthiness balance. We apply this framework to a customer/supplier business network. We show that our trustworthiness score is a significant predictor of the likelihood a business will pay a fine if audited. We show that the market network is characterized by homophily: businesses tend to connect to partners with similar trustworthiness degrees. This suggests that the topology of the network influences the behavior of the actors composing it, indicating that market regulatory efforts should take into account network theory to prevent further degeneration and failures. [ABSTRACT FROM AUTHOR]

Community discovery in complex networks is the task of organizing a network's structure by grouping together nodes related to each other. Traditional approaches are based on the assumption that there is a global-level organization in the network. However, in many scenarios, each node is the bearer of complex information and cannot be classified in disjoint clusters. The top-down global view of the partition approach is not designed for this. Here, we represent this complex information as multiple latent labels, and we postulate that edges in the networks are created among nodes carrying similar labels. The latent labels are the communities a node belongs to and we discover them with a simple local-first approach to community discovery. This is achieved by democratically letting each node vote for the communities it sees surrounding it in its limited view of the global system, its ego neighborhood, using a label propagation algorithm, assuming that each node is aware of the label it shares with each of its connections. The local communities are merged hierarchically, unveiling the modular organization of the network at the global level and identifying overlapping groups and groups of groups. We tested this intuition against the state-of-the-art overlapping community discovery and found that our new method advances in the chosen scenarios in the quality of the obtained communities. We perform a test on benchmark and on real-world networks, evaluating the quality of the community coverage by using the extracted communities to predict the metadata attached to the nodes, which we consider external information about the latent labels. We also provide an explanation about why real-world networks contain overlapping communities and how our logic is able to capture them. Finally, we show how our method is deterministic, is incremental, and has a limited time complexity, so that it can be used on real-world scale networks. [ABSTRACT FROM AUTHOR]