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Social networks form a major parts of people’s lives, and individuals often make important life decisions based on information that spreads through these networks. For this reason, it is important to know whether individuals from different protected groups have equal access to information flowing through a network. In this article, we define the Information Unfairness (IUF) metric, which quantifies inequality in access to information across protected groups. We then introduce MinIUF , an algorithm for reducing inequalities in information flow by adding edges to the network. Finally, we provide an in-depth analysis of information flow with respect to an attribute of interest, such as gender, across different types of networks to evaluate whether the structure of these networks allows groups to equally access information flowing in the network. Moreover, we investigate the causes of unfairness in such networks and how it can be improved. 

It has been observed that real-world social networks often exhibit stratification along economic or other lines, with consequences for class mobility and access to opportunities. With the rise in human interaction data and extensive use of online social networks, the structure of social networks (representing connections between individuals) can be used for measuring stratification. However, although stratification has been studied extensively in the social sciences, there is no single, generally applicable metric for measuring the level of stratification in a network. In this work, we first propose the novel Stratification Assortativity (StA) metric, which measures the extent to which a network is stratified into different tiers. Then, we use the StA metric to perform an in-depth analysis of the stratification of five co-authorship networks. We examine the evolution of these networks over 50 years and show that these fields demonstrate an increasing level of stratification over time, and, correspondingly, the trajectory of a researcher’s career is increasingly correlated with her entry point into the network. 

In the early stages of a pandemic, epidemiological knowledge of the disease is limited and no vaccination is available. This poses the problem of determining an Early Mitigation Strategy. Previous studies have tackled this problem through finding globally influential nodes that contribute the most to the spread. These methods are often not practical due to their assumptions that (1) accessing the full contact social network is possible; (2) there is an unlimited budget for the mitigation strategy; (3) healthy individuals can be isolated for indefinite amount of time, which in practice can have serious mental health and economic consequences. In this work, we study the problem of developing an early mitigation strategy from a community perspective and propose a dynamic Community-based Mitigation strategy, ComMit. The distinguishing features of ComMit are: (1) It is agnostic to the dynamics of the spread; (2) does not require prior knowledge of contact network; (3) it works within a limited budget; and (4) it enforces bursts of short-term restriction on small communities instead of long-term isolation of healthy individuals. ComMit relies on updated data from test-trace reports and its strategy evolves over time. We have tested ComMit on several real-world social networks. The results of our experiments show that, within a small budget, ComMit can reduce the peak of infection by 73% and shorten the duration of infection by 90%, even for spreads that would reach a steady state of non-zero infections otherwise (e.g., SIS contagion model). 

In many network applications, dense subgraphs have proven to be extremely useful. One particular type of dense subgraph known as the k-core has received a great deal of attention. k-cores have been used in a number of important applications, including identifying important nodes, speeding up community detection, network visualization, and others. However, little work has investigated the ‘skeletal’ structure of the k-core, and the effect of such structures on the properties of the overall k-core and network itself. In this paper, we propose the Skeletal Core Subgraph, which describes the backbone of the k-core structure of a graph. We show how to categorize graphs based on their skeletal cores, and demonstrate how to efficiently decompose a given graph into its Skeletal Core Subgraph. We show both theoretically and experimentally the relationship between the Skeletal Core Subgraph and properties of the graph, including its core resilience. 

In many network applications, it may be desirable to conceal certain target nodes from detection by a data collector, who is using a crawling algorithm to explore a network. For example, in a computer network, the network administrator may wish to protect those computers (target nodes) with sensitive information from discovery by a hacker who has exploited vulnerable machines and entered the network. These networks are often protected by hiding the machines (nodes) from external access, and allow only fixed entry points into the system (protection against external attacks). However, in this protection scheme, once one of the entry points is breached, the safety of all internal machines is jeopardized (i.e., the external attack turns into an internal attack). In this paper, we view this problem from the perspective of the data protector. We propose the Node Protection Problem: given a network with known entry points, which edges should be removed/added so as to protect as many target nodes from the data collector as possible? A trivial way to solve this problem would be to simply disconnect either the entry points or the target nodes – but that would make the network non-functional. Accordingly, we impose certain constraints: for each node, only (1 − r) fraction of its edges can be removed, and the resulting network must not be disconnected. We propose two novel scoring mechanisms - the Frequent Path Score and the Shortest Path Score. Using these scores, we propose NetProtect, an algorithm that selects edges to be removed or added so as to best impede the progress of the data collector. We show experimentally that NetProtect outperforms baseline node protection algorithms across several real-world networks. In some datasets, With 1% of the edges removed by NetProtect, we found that the data collector requires up to 6 (4) times the budget compared to the next best baseline in order to discover 5 (50) nodes.