The impact of partially missing communities~on the reliability of centrality measures

Network data is usually not error-free, and the absence of some nodes is a very common type of measurement error. Studies have shown that the reliability of centrality measures is severely affected by missing nodes. This paper investigates the reliability of centrality measures when missing nodes are likely to belong to the same community. We study the behavior of five commonly used centrality measures in uniform and scale-free networks in various error scenarios. We find that centrality measures are generally more reliable when missing nodes are likely to belong to the same community than in cases in which nodes are missing uniformly at random. In scale-free networks, the betweenness centrality becomes, however, less reliable when missing nodes are more likely to belong to the same community. Moreover, centrality measures in scale-free networks are more reliable in networks with stronger community structure. In contrast, we do not observe this effect for uniform networks. Our observations suggest that the impact of missing nodes on the reliability of centrality measures might not be as severe as the literature suggests

A Many-Country Model of Industrialization

We draw attention to the role of economic geography in explaining important cross-sectional facts which are difficult to account for in existing models of industrialization. By construction, closed-economy models that stress the role of local demand in generating sufficient expenditure on manufacturing goods are not suited to explain the strong and negative correlation between distance to the world's main markets and levels of manufacturing activity in the developing world. Secondly, open-economy models that emphasize the importance of comparative advantage are at odds with a positive correlation between the ratio of agricultural to manufacturing productivity and shares of manufacturing in GDP. This paper provides a potential explanation for these puzzles by nesting the above theories in a multi-location model with trade costs. Using a number of simple analytical examples and a full-scale multi-country calibration, we show that the model can replicate the above stylized facts.Industrialization, economic geography, international trade

An Application of Social Network Analysis on Military Strategy, System Networks and the Phases of War

The research developed in this study will utilize Social Network and Graph Theory terminology and methodology applied to groups of systems, rather than individuals within a given system, in order to shape strategic level goals. With regard to military operations, Social Network Analysis has been used to show that enemy networks and relationships can be accurately represented using weighted layers with weighted relationships in order to identify the key player(s) that must be influenced and/or removed so that a particular effect on the enemy might be realized. Social Network Analysis is therefore a significant tool concerning tactical level of operations that aids in developing a targeting methodology which aids tactical commanders in mission planning, however has never been applied to strategic levels of Command. Like previous key player problems, this research will utilize system attributes and global relational strengths as inputs. The output results will rank order representative systems of interest that satisfy the constraints and desired objectives within a particular Phase of War. This work will apply and extend the tools of Social Network Analysis structure and techniques to a theater level mission

Centrality measures for graphons: Accounting for uncertainty in networks

As relational datasets modeled as graphs keep increasing in size and their data-acquisition is permeated by uncertainty, graph-based analysis techniques can become computationally and conceptually challenging. In particular, node centrality measures rely on the assumption that the graph is perfectly known -- a premise not necessarily fulfilled for large, uncertain networks. Accordingly, centrality measures may fail to faithfully extract the importance of nodes in the presence of uncertainty. To mitigate these problems, we suggest a statistical approach based on graphon theory: we introduce formal definitions of centrality measures for graphons and establish their connections to classical graph centrality measures. A key advantage of this approach is that centrality measures defined at the modeling level of graphons are inherently robust to stochastic variations of specific graph realizations. Using the theory of linear integral operators, we define degree, eigenvector, Katz and PageRank centrality functions for graphons and establish concentration inequalities demonstrating that graphon centrality functions arise naturally as limits of their counterparts defined on sequences of graphs of increasing size. The same concentration inequalities also provide high-probability bounds between the graphon centrality functions and the centrality measures on any sampled graph, thereby establishing a measure of uncertainty of the measured centrality score. The same concentration inequalities also provide high-probability bounds between the graphon centrality functions and the centrality measures on any sampled graph, thereby establishing a measure of uncertainty of the measured centrality score.Comment: Authors ordered alphabetically, all authors contributed equally. 21 pages, 7 figure