Magnetic Eigenmaps for the visualization of directed networks

We propose a framework for the visualization of directed networks relying on the eigenfunctions of the magnetic Laplacian, called here Magnetic Eigenmaps. The magnetic Laplacian is a complex deformation of the well-known combinatorial Laplacian. Features such as density of links and directionality patterns are revealed by plotting the phases of the first magnetic eigenvectors. An interpretation of the magnetic eigenvectors is given in connection with the angular synchronization problem. Illustrations of our method are given for both artificial and real networks.The authors thank the following organizations. • EU: The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007–2013)/ERC AdG A-DATADRIVE-B (290923). This paper reflects only the authors’ views, the Union is not liable for any use that may be made of the contained information. • Research Council KUL: GOA/10/09 MaNet, CoE PFV/10/002 (OPTEC), BIL12/11T; PhD/Postdoc grants. • Flemish Govern ment: – FWO: G.0377.12 (Structured systems), G.088114N (Tensor based data similarity); PhD/Postdoc grants. – IWT: SBO POM (100031); PhD/Postdoc grants. • iMinds Medical Information Technologies SBO 2014. • Belgian Federal Science Policy Office: IUAP P7/19 (DYSCO, Dynamical systems, control and optimization, 2012–2017

African Border Disorders

Since the end of the Cold War, the monopoly of legitimate organized force of many African states has been eroded by a mix of rebel groups, violent extremist organizations, and self-defence militias created in response to the rise in organized violence on the continent. African Border Disorders explores the complex relationships that bind states, transnational rebels and extremist organizations, and borders on the African continent. Combining cutting edge network science with geographical analysis, the first part of the book highlights how the fluid alliances and conflicts between rebels, violent extremist organizations and states shape in large measure regional patterns of violence in Africa. The second part of the book examines the spread of Islamist violence around Lake Chad through the lens of the violent Nigerian Islamist group Boko Haram, which has evolved from a nationally-oriented militia group, to an internationally networked organization. The third part of the book explores how violent extremist organizations conceptualize state boundaries and territory and, reciprocally, how do the civil society and the state respond to the rise of transnational organizations. The book will be essential reading for all students and specialists of African politics and security studies, particularly those specializing on fragile states, sovereignty, new wars, and borders as well as governments and international organizations involved in conflict prevention and early intervention in the region

African Border Disorders

Since the end of the Cold War, the monopoly of legitimate organized force of many African states has been eroded by a mix of rebel groups, violent extremist organizations, and self-defence militias created in response to the rise in organized violence on the continent. African Border Disorders explores the complex relationships that bind states, transnational rebels and extremist organizations, and borders on the African continent. Combining cutting edge network science with geographical analysis, the first part of the book highlights how the fluid alliances and conflicts between rebels, violent extremist organizations and states shape in large measure regional patterns of violence in Africa. The second part of the book examines the spread of Islamist violence around Lake Chad through the lens of the violent Nigerian Islamist group Boko Haram, which has evolved from a nationally-oriented militia group, to an internationally networked organization. The third part of the book explores how violent extremist organizations conceptualize state boundaries and territory and, reciprocally, how do the civil society and the state respond to the rise of transnational organizations. The book will be essential reading for all students and specialists of African politics and security studies, particularly those specializing on fragile states, sovereignty, new wars, and borders as well as governments and international organizations involved in conflict prevention and early intervention in the region