Algebraic Connectivity of Interdependent Networks

The algebraic connectivity UN-1, i.e. the second smallest eigenvalue of the Laplacian matrix, plays a crucial role in dynamic phenomena such as diffusion processes, synchronization stability, and network robustness. In this work we study the algebraic connectivity in the general context of interdependent networks, or network-of-networks (NoN)....

Weighted Betweenness and Algebraic Connectivity

One of the better studied topology metrics of complex networks is the second smallest eigenvalue of the Laplacian matrix of a network’s graph, referred to as the algebraic connectivity mN-1. This spectral metric plays a decisive role in synchronization of coupled oscillators, network robustness, consensus problems, belief propagation, graph...

Measuring Robustness of Complex Networks

Specially over the last ten years, societies depend more strongly than ever on networked and communication systems. This dependency has grown to the point to which our well-being depends on these networked critical infrastructures. Bettering our understanding of such complex networks and their robustness is on the bleeding edge of graph theory,...

Robustness Envelopes of Networks

We study the robustness of networks under node removal, considering random node failure, as well as targeted node attacks based on network centrality measures. Whilst both of these have been studied in the literature, existing approaches tend to study random failure in terms of average-case behavior, giving no idea of how badly network...

Generating graphs that approach a prescribed modularity

Modularity is a quantitative measure for characterizing the existence of a community structure in a network. A network's modularity depends on the chosen partitioning of the network into communities, which makes finding the specific partition that leads to the maximum modularity a hard problem. In this paper, we prove that deciding whether a...

Generating graphs that approach a prescribed modularity

Topology dynamics in a P2PTV network

In recent years, a number of commercial peer-to-peer TV (P2PTV) applications have been launched. Yet, their mechanisms and characteristics are unknown. In this paper, we study SopCast, a typical proprietary P2PTV system. Treating SopCast as a black box, we perform a set of experiments that are suitable to analyze SopCast in depth. We attempt to...

Betweenness centrality in a weighted network

A Qualitative Comparison of Power Law Generators