Multimodal freight transport allows switching among different modes of transport to utilize transport facilities more efficiently. This paper proposes an approach on network modeling and robustness assessment for multimodal freight transport networks, where the nodes represent junctions, terminals and crossings, and the links represent pathways. The network model captures the features of interconnection and interdependency. Freight can switch between different modalities at interconnected terminals, while disruption of a single interdependent node (e.g., bridge, tunnel, railway crossing) affects multiple modalities. Considering disruptions of infrastructure elements and capacity degradation of pathways as perturbations, the network robustness is evaluated as the increment of the total travel time caused by these perturbations. We apply our robustness assessment model to the Dutch freight transport, taking into account three modalities: inland waterway, road and railway. The node criticality, defined as the impact of a node removal on the total travel time, resembles a power-law distribution, independent of different traffic assignments. This scale-free property implies a relatively robust state of the network against single random disruptions. Further, we show that the most critical nodes can be roughly identified by their topological properties. Our research helps to schedule the maintenance by assigning priority to the critical infrastructure.

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Optical networks are vulnerable to failures due to targeted attacks or large-scale disasters. The recoverability of optical networks refers to the ability of an optical network to return to a desired performance level after suffering topological perturbations such as link failures. This paper proposes a general topological approach and recoverability indicators to measure the network recoverability for optical networks for two recovery scenarios: 1) only the links which are damaged in the failure process can be recovered and 2) links can be established between any pair of nodes that have no link between them after the failure process. We use the robustness envelopes of realizations and the histograms of two recoverability indicators to illustrate the impact of the random failure and recovery processes on the network performance. By applying the average two-terminal reliability and the network efficiency as robustness metrics, we employ the proposed approach to assess 20 real-world optical networks. Numerical results validate that the network recoverability is coupled to the network topology, the robustness metric and the recovery strategy. We further show that a greedy recovery strategy could provide a near-optimal recovery performance for the robustness metrics. We investigate the sensitivity of network recoverability and find that the sensitivity of the recoverability indicators varies according to different robustness metrics and scenarios. We also find that assortativity has the strongest correlation with both recoverability indicators.@en

The N-Intertwined Mean Field Approximation (NIMFA) is a reasonably accurate approximation of the exact SIS epidemic process on a network. The average fraction of infected nodes in the NIMFA steady state, also called the steady-state prevalence, in terms of the effective infection rate can be expanded into a power series around the NIMFA epidemic threshold. In this paper, we investigate the convergence of the steady-state prevalence Taylor expansion. We determine the radius of convergence in some special types of graphs. We also show that the radius of convergence of the steady-state prevalence expansion depends upon the network topology, in particular, the average degree of the network and the spectral gap of the adjacency matrix play a role.

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Network performance is determined by the interplay of underlying structures and overlying dynamic processes on networks. This thesis mainly considers two types of collective dynamics on networks, spread and transport, which are ubiquitous in our daily lives, ranging from information propagation, disease spreading, to molecular motors on cytoskeleton and urban traffic. Exploring the approaches on optimizing the network performance is the fundamental motivation of this work, which helps to control processes on networks and to upgrade network-based services. Although the properties of phase transition in Susceptible-Infected-Susceptible (SIS) processes have been investigated intensively, the time-dependent behavior of epidemics is still an open question. This thesis starts with the investigation of the spreading time (Chapter 2), which is the time when the number of infected nodes in the metastable state is first reached, starting from the outbreak of the epidemics. We observe that the spreading time resembles a lognormal-like distribution both for the Markovian and the non-Markovian infection processes. As a follow-up work of Chapter 2, we identify the fastest initial spreaders with the shortest average spreading time in epidemics on a network, which helps to ensure an efficient spreading (Chapter 3). We show that the fastest spreader changes with the effective infection rate of a SIS epidemic process, which means that the time-dependent influence of a node is usually strongly coupled to the dynamic process and the underlying network. We propose the spreading efficiency as a metric to quantify the efficiency of a spreader and identify the fastest spreader, which is adaptive to different infection rates in general networks. For maximizing the utility of spread, we introduce induced spreading, which aims to maximize the infection probabilities of some target nodes by adjusting the nodal infection rates (Chapter 4). We assume that the adjustment of the nodal infection rates has an associated cost and formulate the induced spreading for SIS epidemics in networks as an optimization problem under a constraint on the total cost. We address both a static model and a dynamic model for the optimization of the induced SIS spreading. We show that the infection rate increment on each node is coupled to both the degree and the average hops to the target nodes in the static optimization method. In the dynamic method, the effective resistance is a good metric to indicate the minimum total cost for targeting a single node. The average fraction of infected nodes in the NIMFA steady state, also called the steady-state prevalence, in terms of the effective infection rate can be expanded into a power series around the NIMFA epidemic threshold. Practically, we can faster compute the nodal infection probability of the NIMFA steady-state by the truncated expansion with enough terms and an effective infection rate within the radius of convergence. Thus, we investigate the radius of convergence that validates the Taylor expansion of the steady-state prevalence in Chapter 5. We show that the radius of convergence of the steady-state prevalence expansion strongly depends upon the spectral gap of the adjacency matrix. The research on the robustness of transport on networks mainly encompasses two robustness assessment approaches, along with their applications in communication networks and freight transport networks, respectively. Network recoverability refers to the ability of a network to return to a desired performance level after suffering malicious attacks or random failures (Chapter 6). We propose a general topological approach and recoverability indicators to measure the network recoverability in two scenarios: 1) recovery of damaged connections and 2) any disconnected pair of nodes can be connected to each other. By applying the effective graph resistance and the network efficiency as robustness metrics, we employ the proposed approach to assess 10 real-world communication networks. For vehicle transport systems, Chapter 7 proposes a robustness assessment for multimodal transport networks. The representation of interdependent networks is an excellent proxy for the structure of multimodal transportation systems. We apply our robustness assessment model to the Dutch freight transport, taking into account three modalities: waterway, road and railway. The node criticality, defined as the impact of a node removal on the total travel cost, resembles a power-law distribution, which implies scale-free property of the robustness against infrastructure disruptions. Many transport processes have a similar objective that all nodes reach an agreement regarding a certain quantity of interest by exchanging the nodal states with their neighboring nodes, which are described by the consensus model in networks (Chapter 8). The robustness of consensus processes is related to the convergence speed to the stability under external perturbations. The (generalized) algebraic connectivity of a network characterizes the lower-bound of the exponential convergence rate of consensus processes. We investigate the problem of accelerating the convergence of consensus processes by adding links to the network. We propose a greedy strategy for undirected network and further extend our approach to directed networks. Numerical tests verify the better performance of our methods than other metric-based approaches. This thesis considers two dynamic processes on networks and covers performance analysis and optimizations, by means of problem proposal, theoretical analysis, case study and algorithm designing. The developed concepts related to network efficiency and robustness provide a better understanding of collective dynamics on complex networks. The applicability of our methodologies bridges theoretical network models and realistic applications, as well as demonstrates the promising efficacy of network science.@en

In this paper, we propose closed-form analytic approximations for the minimum number of driver nodes needed to fully control networks, where links are removed according to both random and targeted attacks. Our approximations rely on the concept of critical links. A link is called critical if its removal increases the required number of driver nodes. We validate our approximation on both real-world and synthetic networks. For random attacks, the approximation is always very good, as long as the fraction of removed links is smaller than the fraction of critical links. For some cases, the approximation is still accurate for larger fractions of removed links. The approximation for an attack, where first the critical links are removed, is also accurate, as long as the fraction of removed links is sufficiently small. Finally, we show that the critical link attack is the most effective among 4 considered attacks, as long as the fraction of removed links is smaller than the fraction of critical links. @en

Network recoverability refers to the ability of a network to return to a desired performance level after suffering malicious attacks or random failures. This paper proposes a general topological approach and recoverability indicators to measure the network recoverability in two scenarios: 1) recovery of damaged connections and 2) any disconnected pair of nodes can be connected to each other. Our approach presents the effect of the random attack and recovery processes on the network performance by the robustness envelopes of realizations and the histograms of two recoverability indicators. By applying the effective graph resistance and the network efficiency as robustness metrics, we employ the proposed approach to assess 10 realworld communication networks. Numerical results verify that the network recoverability is coupled to the network topology, the robustness metric and the recovery strategy. We also show that a greedy recovery strategy could provide a near-optimal recovery performance for the investigated robustness metrics.

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Identifying the fastest spreaders in epidemics on a network helps to ensure an efficient spreading. By ranking the average spreading time for different spreaders, we show that the fastest spreader may change with the effective infection rate of a SIS epidemic process, which means that the time-dependent influence of a node is usually strongly coupled to the dynamic process and the underlying network. With increasing effective infection rate, we illustrate that the fastest spreader changes from the node with the largest degree to the node with the shortest flooding time. (The flooding time is the minimum time needed to reach all other nodes if the process is reduced to a flooding process.) Furthermore, by taking the local topology around the spreader and the average flooding time into account, we propose the spreading efficiency as a metric to quantify the efficiency of a spreader and identify the fastest spreader, which is adaptive to different infection rates in general networks.

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In a Susceptible–Infected–Susceptible (SIS) process, we investigate the spreading time T_m, which is the time when the number of infected nodes in the metastable state is first reached, starting from the outbreak of the epidemics. We observe that the spreading time T_m resembles a lognormal-like distribution, though with different deep tails, both for the Markovian and the non-Markovian infection process, which implies that the spreading time can be very long with a relatively high probability. In addition, we show that a stronger virus, with a higher effective infection rate τ or an earlier timing of the infection attempts, does not always lead to a shorter average spreading time E[T_m]. We numerically demonstrate that the average spreading time E[T_m] in the complete graph and the star graph scales logarithmically as a function of the network size N for a fixed fraction of infected nodes in the metastable state.

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Induced spreading aims to maximize the infection probabilities of some target nodes by adjusting the nodal infection rates, which can be applied in biochemical and information spreading. We assume that the adjustment of the nodal infection rates has an associated cost and formulate the induced spreading for SIS epidemics in networks as an optimization problem under a constraint on total cost. We address and solve both a static model and a dynamic model for the optimization of the induced SIS spreading. By numerical results in some artificial and real networks, we investigate the effect of the network topology on the optimal induced strategy with a quadratic cost function. In the static method, the infection rate increment on each node is coupled to both the degree and the average hops to the targets. In the dynamic method, we show that the effective resistance could be a good metric to indicate the minimum total cost for targeting a single node. We also illustrate that the minimum total cost increases much more slowly with the increasing fraction of targets in the SIS model than in linear control systems.@en