Quantifying the Robustness of Complex Networks with Heterogeneous Nodes

The robustness of a complex network measures its ability to withstand random or targeted attacks. Most network robustness measures operate under the assumption that the nodes in a network are homogeneous and abstract. However, most real-world networks consist of nodes that are heterogeneous in nature. In this work, we propose a robustness measure called fitness-incorporated average network efficiency, that attempts to capture the heterogeneity of nodes using the `fitness’ of nodes in measuring the robustness of a network. Further, we adopt the same measure to compare the robustness of networks with heterogeneous nodes under varying topologies, such as the scale-free topology or the Erdős–Rényi random topology. We apply the proposed robustness measure using a wireless sensor network simulator to show that it can be effectively used to measure the robustness of a network using a topological approach. We also apply the proposed robustness measure to two real-world networks; namely the CO2 exchange network and an air traffic network. We conclude that with the proposed measure, not only the topological structure, but also the fitness function and the fitness distribution among nodes, should be considered in evaluating the robustness of a complex network.

A robust optimization model for influence maximization in social networks with heterogeneous nodes

Influence maximization is the problem of trying to maximize the number of influenced nodes by selecting optimal seed nodes, given that influencing these nodes is costly. Due to the probabilistic nature of the problem, existing approaches deal with the concept of the expected number of nodes. In the current research, a scenario-based robust optimization approach is taken to finding the most influential nodes. The proposed robust optimization model maximizes the number of infected nodes in the last step of diffusion while minimizing the number of seed nodes. Nodes, however, are treated as heterogeneous with regard to their propensity to pass messages along; or as having varying activation thresholds. Experiments are performed on a real text-messaging social network. The model developed here significantly outperforms some of the well-known existing heuristic approaches which are proposed in previous works.

Failure propagation in interdependent multi-level networks

В этой работе разрабатываются новый подход и алгоритмические инструменты для моделирования и анализа живучести сетей с разнородными узлами, а также рассматривается их применение в космических сетях. Космические сети позволяют совместно использовать ресурсы космических аппаратов на орбите, такие как хранение, обработка и обмен данными. Каждый космический аппарат в сети может иметь различный состав и функциональность подсистем, что приводит к неоднородности узлов. Большинство традиционных анализов живучести сетей предполагают однородность узлов и в результате не подходят для анализа космических сетей. Эта работа предполагает, что гетерогенные сети могут быть смоделированы как взаимозависимые многоуровневые сети, что позволяет проводить анализ их живучести. Многоуровневый аспект фиксирует разбивку сети в соответствии с общими функциональными возможностями в различных узлах и позволяет создавать однородные подсети, в то время как аспект взаимозависимости ограничивает сеть для захвата физических характеристик каждого узла. In this paper, we develop a new approach and algorithmic tools for modeling and analyzing the survivability of networks with heterogeneous nodes, and also consider their application in space networks. Space networks allow the sharing of spacecraft resources in orbit, such as data storage, processing, and exchange. Each spacecraft in the network may have a different composition and functionality of subsystems, which leads to heterogeneity of nodes. Most traditional network survivability analyses assume node homogeneity and as a result are not suitable for space network analysis. This work suggests that heterogeneous networks can be modeled as interdependent multi-level networks, allowing analysis of their survivability. The multi-level aspect captures the network breakdown according to the common functionality in different nodes and allows for the creation of homogeneous subnets, while the interdependence aspect restricts the network to capture the physical characteristics of each node.

HeterSkinNet

Character rigging is universally needed in computer graphics but notoriously laborious. We present a new method, HeterSkinNet, aiming to fully automate such processes and significantly boost productivity. Given a character mesh and skeleton as input, our method builds a heterogeneous graph that treats the mesh vertices and the skeletal bones as nodes of different types and uses graph convolutions to learn their relationships. To tackle the graph heterogeneity, we propose a new graph network convolution operator that transfers information between heterogeneous nodes. The convolution is based on a new distance HollowDist that quantifies the relations between mesh vertices and bones. We show that HeterSkinNet is robust for production characters by providing the ability to incorporate meshes and skeletons with arbitrary topologies and morphologies (e.g., out-of-body bones, disconnected mesh components, etc.). Through exhaustive comparisons, we show that HeterSkinNet outperforms state-of-the-art methods by large margins in terms of rigging accuracy and naturalness. HeterSkinNet provides a solution for effective and robust character rigging.