Low Average Shortest Path Length Research Articles

Evaluation of network expansion decisions for resilient interdependent critical infrastructures with different topologies

Resilient interdependent critical infrastructures (CIs) can better withstand cascading failures in disruptive events. This study proposes network expansion as a resilience improvement strategy for interdependent CIs and evaluates the influence of topology in interdependent network design for resilience optimization under disruption uncertainty. A resilience score consisting of network complexity and unmet demand metrics is introduced to quantify the resilience of expanded networks. Five synthetic interdependent network instances with random and hub-and-spoke (i.e., cluster) topologies are generated to represent CIs with heterogeneous node functions. Different network expansion opportunities are considered and critical node disruption scenarios are used to evaluate the impact of uncertain disruptions. We apply a two-stage stochastic multi-objective resilience optimization model to determine strategic investment decisions using the expected total cost and expected resilience score as competing objectives. Compromise solutions of expanded network designs are identified from Pareto optimal solutions and they are characterized according to their graph properties. The results show that expanded networks have improved resilience and the extent of improvement is affected by the network topology and type of disruption. Under critical node disruptions, a random network is more resilient than a hub-and-spoke structure due to its better connectivity. Characteristics of highly connected interdependent networks are high average node degree, high clustering coefficient, and low average shortest path length. Resilience improvement is more limited in expanded networks with a hub-and-spoke structure due to the negative impact of hub failures.

The social networks of free-roaming domestic dogs in island communities in the Torres Strait, Australia

Social structure creates heterogeneity of interactions between individuals, thus influencing infectious disease spread. The objective of this study was to describe and characterise the social structure of free-roaming dog populations in three communities in the Torres Strait, Australia.Dogs in Kubin, Saibai, and Warraber communities were collared with GPS units that recorded locations at 15 s intervals for up to 1 week, and datasets were obtained from 24 (62% of the dog population), 23 (53%) and 21 (51%) dogs in each community, respectively. An association (potential contact) between dogs was defined as proximity within a spatio-temporal window of 5 m for 30 s. Networks were constructed for each dog population: 1. nodes were individual dogs, and 2. edges were weighted according to the duration of spatio-temporal association between pairs of dogs as a proportion of their simultaneous time monitored. Network statistics were calculated for each population and the robustness of networks to the duration of association between pairs of dogs was assessed in terms of efficiency, degree distribution and fragmentation (number of components).Dog social networks had ‘small-world’ structures, with characteristic clustering and low average shortest-path length between individuals. Overall, all three networks were highly connected in terms of degree distribution and global and local efficiency, but the median tie strength (2–13.5 min) was low. Centrality and the duration of association (tie-strength) between dogs were significantly different between communities. The Kubin network was least robust to fragmentation when ties of short duration were successively removed (14 components with minimum tie strength of 2 h). In contrast, the Warraber dog network was relatively robust with 7 components at minimum tie strength of 2 h as well as high local efficiency within components.We conclude that whilst infectious disease that requires a short duration of contact for transmission is likely to spread rapidly between and within clusters in all three networks in this study, fragmentation of networks ― once ties of short duration are removed ― is likely to limit spread of disease that requires a longer duration of direct contact. The network information in this study is useful as a foundation for disease spread modelling and to investigate control strategies such as movement restrictions in dog populations.

Design of optimal nonlinear network controllers for Alzheimer's disease.

Brain stimulation can modulate the activity of neural circuits impaired by Alzheimer’s disease (AD), having promising clinical benefit. However, all individuals with the same condition currently receive identical brain stimulation, with limited theoretical basis for this generic approach. In this study, we introduce a control theory framework for obtaining exogenous signals that revert pathological electroencephalographic activity in AD at a minimal energetic cost, while reflecting patients’ biological variability. We used anatomical networks obtained from diffusion magnetic resonance images acquired by the Alzheimer’s Disease Neuroimaging Initiative (ADNI) as mediators for the interaction between Duffing oscillators. The nonlinear nature of the brain dynamics is preserved, given that we extend the so-called state-dependent Riccati equation control to reflect the stimulation objective in the high-dimensional neural system. By considering nonlinearities in our model, we identified regions for which control inputs fail to correct abnormal activity. There are changes to the way stimulated regions are ranked in terms of the energetic cost of controlling the entire network, from a linear to a nonlinear approach. We also found that limbic system and basal ganglia structures constitute the top target locations for stimulation in AD. Patients with highly integrated anatomical networks–namely, networks having low average shortest path length, high global efficiency–are the most suitable candidates for the propagation of stimuli and consequent success on the control task. Other diseases associated with alterations in brain dynamics and the self-control mechanisms of the brain can be addressed through our framework.

A network theoretic study of ecological connectivity in Western Himalayas

Network theoretic approach has been used to model and study the flow of ecological information, growth and connectivity on landscape level of anemochory (wind dispersal) of Himalayan moist temperate forest species in the Western Himalaya region. A network is formally defined and derived for seed dispersion model of target floral species where vertices represent habitat patches which are connected by an edge if the distance between the patches is less than a threshold distance. We define centrality of a network and computationally identify the habitat patches that are central to the process of seed dispersion to occur across the network. These central patches are located on map and geographical regions critically important for the flow of ecological information across the network are identified as Gharwal region and eastern Himachal Pradesh of Indian Himalaya. We find that the network of habitat patches is a scale-free network and at the same time it also displays small-world property characterized by high clustering and low average shortest path length. As a result, ecological information propagates rapidly and evenly on a local scale. Hubs in the network are identified as important centres for dissemination of ecological information (seeds) and need to be conserved against a potential attack by malicious agents and also ecological shocks. The network showcase a well-formed community structure. As a consequence of these structural properties of the network, anemochory floral species studied in this work are likely to thrive across the ecological network of forest patches in the Western Himalaya region over time.

Distributed Shortcut Networks: Low-Latency Low-Degree Non-Random Topologies Targeting the Diameter and Cable Length Trade-Off

Low communication latency becomes a main concern in highly parallel computers and supercomputers that reach millions of processing cores. Random network topologies are better suited to achieve low average shortest path length and low diameter in terms of the hop counts between nodes. However, random topologies lead to two problems: (1) increased aggregate cable length on a machine room floor that would become dominant for communication latency in next-generation custom supercomputers, and (2) high routing complexity that typically requires a routing table at each node (e.g., topology-agnostic deadlock-free routing). In this context, we first propose low-degree non-random topologies that exploit the small-world effect, which has been well modeled by some random network models. Our main idea is to carefully design a set of various-length shortcuts that keep the diameter small while maintaining a short cable length for economical passive electric cables. We also propose custom routing that uses the regularity of the various-length shortcuts. Our experimental graph analyses show that our proposed topology has low diameter and low average shortest path length, which are considerably better than those of the counterpart 3-D torus and are near to those of a random topology with the same average degree. The proposed topology has average cable length drastically shorter than that of the counterpart random topology, which leads to low cost of interconnection networks. Our custom routing takes non-minimal paths to provide lower zero-load latency than the minimal custom routings on different counterpart topologies. Our discrete-event simulation results using SimGrid show that our proposed topology is suitable for applications that have irregular communication patterns or non-nearest neighbor collective communication patterns.

On the topologic structure of economic complex networks: Empirical evidence from large scale payment network of Estonia

This paper presents the first topological analysis of the economic structure of an entire country based on payments data obtained from Swedbank. This data set is exclusive in its kind because around 80% of Estonia's bank transactions are done through Swedbank; hence, the economic structure of the country can be reconstructed. Scale-free networks are commonly observed in a wide array of different contexts such as nature and society. In this paper, the nodes are comprised by customers of the bank (legal entities) and the links are established by payments between these nodes. We study the scaling-free and structural properties of this network. We also describe its topology, components and behaviors. We show that this network shares typical structural characteristics known in other complex networks: degree distributions follow a power law, low clustering coefficient and low average shortest path length. We identify the key nodes of the network and perform simulations of resiliency against random and targeted attacks of the nodes with two different approaches. With this, we find that by identifying and studying the links between the nodes is possible to perform vulnerability analysis of the Estonian economy with respect to economic shocks.