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Measuring robustness is a fundamental task for analyzing the structure of complex networks. Indeed, several approaches to capture the robustness properties of a network have been proposed. In this paper we focus on spectral graph theory…
Graph rigidity theory is an important tool for examining the solvability of sensor network localization (SNL) problems, and ensuring global convergence of localization algorithms. Along this direction, diverse measurements such as signed…
Network robustness research aims at finding a measure to quantify network robustness. Once such a measure has been established, we will be able to compare networks, to improve existing networks and to design new networks that are able to…
In weighted graphs the shortest path between two nodes is often reached through an indirect path, out of all possible connections, leading to structural redundancies which play key roles in the dynamics and evolution of complex networks. We…
Graph rigidity theory studies the capability of a graph embedded in the Euclidean space to constrain its global geometric shape via local constraints among nodes and edges, and has been widely exploited in network localization and formation…
Robustness is a critical measure of the resilience of large networked systems, such as transportation and communication networks. Most prior works focus on the global robustness of a given graph at large, e.g., by measuring its overall…
This article examines the application of a popular measure of sparsity, Gini Index, on network graphs. A wide variety of network graphs happen to be sparse. But the index with which sparsity is commonly measured in network graphs is edge…
Studying network robustness for wireless sensor networks(WSNs) is an exciting topic of research as sensor nodes often fail due to hardware degradation, resource constraints, and environmental changes. The application of spectral graph…
This paper presents a framework addressing the challenge of global localization in autonomous mobile robotics by integrating LiDAR-based descriptors and Wi-Fi fingerprinting in a pre-mapped environment. This is motivated by the increasing…
In this work, water distribution systems are regarded as large sparse planar graphs with complex network characteristics and the relationship between important topological features of the network (i.e. structural robustness and loop…
In this paper, we study the redundancy of linear codes with graph constraints. First we consider linear parity check codes based on bipartite graphs with diversity and with generalized graph constraints. We describe sufficient conditions on…
This paper introduces a novel algorithm for cardinality, i.e., the number of nodes, estimation in large scale anonymous graphs using statistical inference methods. Applications of this work include estimating the number of sensor devices,…
The study of network robustness is a critical tool in the characterization and sense making of complex interconnected systems such as infrastructure, communication and social networks. While significant research has been conducted in all of…
Networks are inherently vulnerable to vertex failures, making the analysis of their structural robustness a fundamental problem in graph theory. In this study, we investigate the closeness and vertex residual closeness of graphs, with a…
We investigate a special case of hereditary property in graphs, referred to as {\em robustness}. A property (or structure) is called robust in a graph $G$ if it is inherited by all the connected spanning subgraphs of $G$. We motivate this…
Redundancy needs more precise characterization as it is a major factor in the evolution and robustness of networks of multivariate interactions. We investigate the complexity of such interactions by inferring a connection transitivity that…
We introduce the concept of natural connectivity as a robustness measure of complex networks. The natural connectivity has a clear physical meaning and a simple mathematical formulation. It characterizes the redundancy of alternative paths…
A smartphone-based user mobility tracking could be effective in finding his/her location, while the unpredictable error therein due to low specification of built-in inertial measurement units (IMUs) rejects its standalone usage but demands…
Connectivity of wireless sensor networks (WSNs) is a fundamental global property expected to be maintained even though some sensor nodes are at fault. In this paper, we investigate the connectivity of random geometric graphs (RGGs) in the…
This paper investigates the localization problem of a network in 2-D and 3-D spaces given the positions of anchor nodes in a global frame and inter-node relative measurements in local coordinate frames. It is assumed that the local frames…