Characterizing Distances of Networks on the Tensor Manifold

At the core of understanding dynamical systems is the ability to maintain and control the systems behavior that includes notions of robustness, heterogeneity, or regime-shift detection. Recently, to explore such functional properties, a convenient representation has been to model such dynamical systems as a weighted graph consisting of a finite, but very large number of interacting agents. This said, there exists very limited relevant statistical theory that is able cope with real-life data, i.e., how does perform analysis and/or statistics over a family of networks as opposed to a specific network or network-to-network variation. Here, we are interested in the analysis of network families whereby each network represents a point on an underlying statistical manifold. To do so, we explore the Riemannian structure of the tensor manifold developed by Pennec previously applied to Diffusion Tensor Imaging (DTI) towards the problem of network analysis. In particular, while this note focuses on Pennec definition of geodesics amongst a family of networks, we show how it lays the foundation for future work for developing measures of network robustness for regime-shift detection. We conclude with experiments highlighting the proposed distance on synthetic networks and an application towards biological (stem-cell) systems.Comment: This paper is accepted at 8th International Conference on Complex Networks 201

Percolation theory applied to measures of fragmentation in social networks

We apply percolation theory to a recently proposed measure of fragmentation $F$ for social networks. The measure $F$ is defined as the ratio between the number of pairs of nodes that are not connected in the fragmented network after removing a fraction $q$ of nodes and the total number of pairs in the original fully connected network. We compare $F$ with the traditional measure used in percolation theory, $P_{\infty}$, the fraction of nodes in the largest cluster relative to the total number of nodes. Using both analytical and numerical methods from percolation, we study Erd\H{o}s-R\'{e}nyi (ER) and scale-free (SF) networks under various types of node removal strategies. The removal strategies are: random removal, high degree removal and high betweenness centrality removal. We find that for a network obtained after removal (all strategies) of a fraction $q$ of nodes above percolation threshold, $P_{\infty}\approx (1-F)^{1/2}$. For fixed $P_{\infty}$ and close to percolation threshold ($q=q_c$), we show that $1-F$ better reflects the actual fragmentation. Close to $q_c$, for a given $P_{\infty}$, $1-F$ has a broad distribution and it is thus possible to improve the fragmentation of the network. We also study and compare the fragmentation measure $F$ and the percolation measure $P_{\infty}$ for a real social network of workplaces linked by the households of the employees and find similar results.Comment: submitted to PR

A New Order of Things: Network Mechanisms of Field Evolution in the Aftermath of an Exogenous Shock

This study examines the role of a major environmental shock in triggering change in the social structure of an organizational field. Based on the longitudinal analysis of changing network configurations in the global airline industry, we explore how logics of attachment shift before, during and after an exogenous shock and how the rewiring of network ties in response to the shock may act as a countervailing force to the network dynamics that drive field stratification. Using the terrorist attacks of September 11, 2001 as a natural experiment, our work reveals how shocks may affect key mechanisms of network evolution thus altering tie distribution and access among members of the field. Overall this article contributes to emergent literature on field dynamics by exposing the evolution of interorganizational dynamics when external events produce unsettled times that render extant logics brittle and open prospects for change

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

Analysing the correlation between social network analysis measures and performance of students in social network-based engineering education

Social network-based engineering education (SNEE) is designed and implemented as a model of Education 3.0 paradigm. SNEE represents a new learning methodology, which is based on the concept of social networks and represents an extended model of project-led education. The concept of social networks was applied in the real-life experiment, considering two different dimensions: (1) to organize the education process as a social network-based process; and (2) to analyze the students' interactions in the context of evaluation of the students learning performance. The objective of this paper is to present a new model for students evaluation based on their behavior during the course and its validation in comparison with the traditional model of students' evaluation. The validation of the new evaluation model is made through an analysis of the correlation between social network analysis measures (degree centrality, closeness centrality, betweenness centrality, eigenvector centrality, and average tie strength) and the grades obtained by students (grades for quality of work, grades for volume of work, grades for diversity of work, and final grades) in a social network-based engineering education. The main finding is that the obtained correlation results can be used to make the process of the students' performance evaluation based on students interactions (behavior) analysis, to make the evaluation partially automatic, increasing the objectivity and productivity of teachers and allowing a more scalable process of evaluation. The results also contribute to the behavioural theory of learning performance evaluation. More specific findings related to the correlation analysis are: (1) the more different interactions a student had (degree centrality) and the more frequently the student was between the interaction paths of other students (betweenness centrality), the better was the quality of the work; (2) all five social network measures had a positive and strong correlation with the grade for volume of work and with the final graThe authors wish to acknowledge the support of the Fundacao para a Ciencia e Tecnologia (FCT), Portugal, through the Grants "Projeto Estrategico-UI 252-2011-2012'' reference PEst-OE/EME/UI0252/2011, "Ph.D. Scholarship Grant'' reference SFRH/BD/85672/2012, and the support of Parallel Planes Lda.info:eu-repo/semantics/publishedVersio

Inferring Social Ties in Academic Networks Using Short-Range Wireless Communications

International audienceWiFi base stations are increasingly deployed in both public spaces and private companies, and the increase in their density poses a significant threat to the privacy of connected users. Prior studies have provided evidence that it is possible to infer the social ties of users from their location and co-location traces but they lack one important component: the comparison of the inference accuracy between an internal attacker (e.g., a curious application running on a mobile device) and a realistic external eavesdropper in the same field trial. In this paper, we experimentally show that such an eavesdropper is able to infer the type of social relationships between mobile users better than an internal attacker. Moreover, our results indicate that by exploiting the underlying social community structure of mobile users, the accuracy of the inference attacks doubles. Based on our findings, we propose countermeasures to help users protect their privacy against eavesdroppers

A social network approach to examine K-12 educational leaders’ influence on information diffusion on Twitter

This study investigated the relationship between the leader’s gender, leadership position, Twitter use, and influence on information diffusion in the communication network on Twitter. We collected the 30,200 latest tweets of 151 active Twitter users who held educational leadership positions. Results of social network analysis and multiple regression analyses suggest a gender inequality in the leader’s influence on information diffusion in the network. Findings also indicate no significant relationship between leadership position (district vs. building) and a leader\u27s influence in the network. Moreover, Twitter following was positively associated with the leader’s influence in the network, whereas the number of followers, weekly tweets, and the time of Twitter account creation did not predict the leader’s influence. Practical implications on how leaders use Twitter to disseminate information are discussed

Acquisizione di rumore sismico nell'Appennino Reggiano Modenese 11-15 aprile 2006

Tra l’11 e il 15 aprile 2006 è stata condotta una campagna di acquisizione di rumore sismico in alcuni siti in frana dell’Appennino Settentrionale. Lo scopo dell’esperimento è quello di stimare gli effetti di sito su corpi franosi tipici dell’Appennino Modenese e Reggiano, nonché di studiare il comportamento delle frane quando sono soggette ad eventi sismici. Le registrazioni di rumore sono state effettuate con stazioni equipaggiate con sensori a corto periodo a tre componenti. Per la stima dell’amplificazione locale è stata scelta una serie di siti caratterizzati da litologie diverse. Inoltre, in siti omogenei e ben studiati dal punto di vista strutturale, sono state effettuate delle misure di rumore in configurazione di array per la stima di un modello di velocità superficiale, allo scopo di confrontare i risultati sperimentali con le funzioni di trasferimento teoriche. La durata delle registrazione non è stata inferiore ad un’ora per ogni sito. Le misure sono state effettuate sulle frane di Ca’ Lita (MO), Cavola (RE) e La Lezza Nuova (RE). Tutte e tre sono frane da colata, caratterizzate dalla presenza in superficie di strati di argille, e sono state studiate dal punto di vista strutturale, tra l’altro attraverso pozzi di sondaggio ed esperimenti di sismica attiva