124 research outputs found
On the influence of topological characteristics on robustness of complex networks
In this paper, we explore the relationship between the topological
characteristics of a complex network and its robustness to sustained targeted
attacks. Using synthesised scale-free, small-world and random networks, we look
at a number of network measures, including assortativity, modularity, average
path length, clustering coefficient, rich club profiles and scale-free exponent
(where applicable) of a network, and how each of these influence the robustness
of a network under targeted attacks. We use an established robustness
coefficient to measure topological robustness, and consider sustained targeted
attacks by order of node degree. With respect to scale-free networks, we show
that assortativity, modularity and average path length have a positive
correlation with network robustness, whereas clustering coefficient has a
negative correlation. We did not find any correlation between scale-free
exponent and robustness, or rich-club profiles and robustness. The robustness
of small-world networks on the other hand, show substantial positive
correlations with assortativity, modularity, clustering coefficient and average
path length. In comparison, the robustness of Erdos-Renyi random networks did
not have any significant correlation with any of the network properties
considered. A significant observation is that high clustering decreases
topological robustness in scale-free networks, yet it increases topological
robustness in small-world networks. Our results highlight the importance of
topological characteristics in influencing network robustness, and illustrate
design strategies network designers can use to increase the robustness of
scale-free and small-world networks under sustained targeted attacks
Evolutionary stable strategies in networked games: the influence of topology
Evolutionary game theory is used to model the evolution of competing
strategies in a population of players. Evolutionary stability of a strategy is
a dynamic equilibrium, in which any competing mutated strategy would be wiped
out from a population. If a strategy is weak evolutionarily stable, the
competing strategy may manage to survive within the network. Understanding the
network-related factors that affect the evolutionary stability of a strategy
would be critical in making accurate predictions about the behaviour of a
strategy in a real-world strategic decision making environment. In this work,
we evaluate the effect of network topology on the evolutionary stability of a
strategy. We focus on two well-known strategies known as the Zero-determinant
strategy and the Pavlov strategy. Zero-determinant strategies have been shown
to be evolutionarily unstable in a well-mixed population of players. We
identify that the Zero-determinant strategy may survive, and may even dominate
in a population of players connected through a non-homogeneous network. We
introduce the concept of `topological stability' to denote this phenomenon. We
argue that not only the network topology, but also the evolutionary process
applied and the initial distribution of strategies are critical in determining
the evolutionary stability of strategies. Further, we observe that topological
stability could affect other well-known strategies as well, such as the general
cooperator strategy and the cooperator strategy. Our observations suggest that
the variation of evolutionary stability due to topological stability of
strategies may be more prevalent in the social context of strategic evolution,
in comparison to the biological context
Higher order assortativity in complex networks
Assortativity was first introduced by Newman and has been extensively studied
and applied to many real world networked systems since then. Assortativity is a
graph metrics and describes the tendency of high degree nodes to be directly
connected to high degree nodes and low degree nodes to low degree nodes. It can
be interpreted as a first order measure of the connection between nodes, i.e.
the first autocorrelation of the degree-degree vector. Even though
assortativity has been used so extensively, to the author's knowledge, no
attempt has been made to extend it theoretically. This is the scope of our
paper. We will introduce higher order assortativity by extending the Newman
index based on a suitable choice of the matrix driving the connections. Higher
order assortativity will be defined for paths, shortest paths, random walks of
a given time length, connecting any couple of nodes. The Newman assortativity
is achieved for each of these measures when the matrix is the adjacency matrix,
or, in other words, the correlation is of order 1. Our higher order
assortativity indexes can be used for describing a variety of real networks,
help discriminating networks having the same Newman index and may reveal new
topological network features.Comment: 24 pages, 16 figure
The failure tolerance of mechatronic software systems to random and targeted attacks
This paper describes a complex networks approach to study the failure
tolerance of mechatronic software systems under various types of hardware
and/or software failures. We produce synthetic system architectures based on
evidence of modular and hierarchical modular product architectures and known
motifs for the interconnection of physical components to software. The system
architectures are then subject to various forms of attack. The attacks simulate
failure of critical hardware or software. Four types of attack are
investigated: degree centrality, betweenness centrality, closeness centrality
and random attack. Failure tolerance of the system is measured by a 'robustness
coefficient', a topological 'size' metric of the connectedness of the attacked
network. We find that the betweenness centrality attack results in the most
significant reduction in the robustness coefficient, confirming betweenness
centrality, rather than the number of connections (i.e. degree), as the most
conservative metric of component importance. A counter-intuitive finding is
that "designed" system architectures, including a bus, ring, and star
architecture, are not significantly more failure-tolerant than interconnections
with no prescribed architecture, that is, a random architecture. Our research
provides a data-driven approach to engineer the architecture of mechatronic
software systems for failure tolerance.Comment: Proceedings of the 2013 ASME International Design Engineering
Technical Conferences & Computers and Information in Engineering Conference
IDETC/CIE 2013 August 4-7, 2013, Portland, Oregon, USA (In Print
Percolation Centrality: Quantifying Graph-Theoretic Impact of Nodes during Percolation in Networks
A number of centrality measures are available to determine the relative importance of a node in a complex network, and betweenness is prominent among them. However, the existing centrality measures are not adequate in network percolation scenarios (such as during infection transmission in a social network of individuals, spreading of computer viruses on computer networks, or transmission of disease over a network of towns) because they do not account for the changing percolation states of individual nodes. We propose a new measure, percolation centrality, that quantifies relative impact of nodes based on their topological connectivity, as well as their percolation states. The measure can be extended to include random walk based definitions, and its computational complexity is shown to be of the same order as that of betweenness centrality. We demonstrate the usage of percolation centrality by applying it to a canonical network as well as simulated and real world scale-free and random networks. © 2013 Piraveenan et al.published_or_final_versio
Topological analysis of longitudinal networks
Longitudinal networks evolve over time through the addition or deletion of nodes and edges. A longitudinal network can be viewed as a single static network that aggregates all edges observed over some time period (i.e., structure of network is fixed), or as a series of static networks observed in different point of time over the entire network observation period (i.e., structure of network is changing over time). By following a topological approach (i.e., static topology and dynamic topology), this paper first proposes a framework to analyze longitudinal networks. In static topology, SNA methods are applied to the aggregated network of entire observation period. Smaller segments of network data (i.e., short-interval network) that are accumulated in less time compared to the entire network observation period are used in dynamic topology for analysis purpose. Based on this framework, this study then conducts a topological analysis of email communication networks of an organization during its different operational conditions to explore changes in the behavior of actor-level dynamics. © 2012 IEEE.published_or_final_versio
Impact of network assortativity on epidemic and vaccination behaviour
The resurgence of measles is largely attributed to the decline in vaccine
adoption and the increase in mobility. Although the vaccine for measles is
readily available and highly successful, its current adoption is not adequate
to prevent epidemics. Vaccine adoption is directly affected by individual
vaccination decisions, and has a complex interplay with the spatial spread of
disease shaped by an underlying mobility (travelling) network. In this paper,
we model the travelling connectivity as a scale-free network, and investigate
dependencies between the network's assortativity and the resultant epidemic and
vaccination dynamics. In doing so we extend an SIR-network model with
game-theoretic components, capturing the imitation dynamics under a voluntary
vaccination scheme. Our results show a correlation between the epidemic
dynamics and the network's assortativity, highlighting that networks with high
assortativity tend to suppress epidemics under certain conditions. In highly
assortative networks, the suppression is sustained producing an early
convergence to equilibrium. In highly disassortative networks, however, the
suppression effect diminishes over time due to scattering of non-vaccinating
nodes, and frequent switching between the predominantly vaccinating and
non-vaccinating phases of the dynamics.Comment: 17 pages, 13 figure
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