Mahendra Piraveenan

Assortative Mixing in Directed Biological Networks

We analyze assortative mixing patterns of biological networks which are typically directed. We develop a theoretical background for analyzing mixing patterns in directed networks before applying them to specific biological networks. Two new quantities are introduced, namely the in-assortativity and the out-assortativity, which are shown to be useful in quantifying assortative mixing in directed networks. We also introduce the local (node level) assortativity quantities for in- and out-assortativity. Local assortativity profiles are the distributions of these local quantities over node degrees and can be used to analyze both canonical and real-world directed biological networks. Many biological networks, which have been previously classified as disassortative, are shown to be assortative with respect to these new measures. Finally, we demonstrate the use of local assortativity profiles in analyzing the functionalities of particular nodes and groups of nodes in real-world biological networks.

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.

Measuring topological robustness of networks under sustained targeted attacks

In this paper, we introduce a measure to analyse the structural robustness of complex networks, which is specifically applicable in scenarios of targeted, sustained attacks. The measure is based on the changing size of the largest component as the network goes through disintegration. We argue that the measure can be used to quantify and compare the effectiveness of various attack strategies. Applying this measure, we confirm the result that scale-free networks are comparatively less vulnerable to random attacks and more vulnerable to targeted attacks. Then we analyse the robustness of a range of real world networks, and show that most real world networks are least robust to attacks based on betweenness of nodes. We also show that the robustness of some networks are more sensitive to the attack strategy compared to others, and given the disparity in the computational complexities of calculating various centrality measures, the robustness coefficient introduced can play a key role in choosing the attack and defence strategies for real world networks. While the measure is applicable to all types of complex networks, we clearly demonstrate its relevance to social network analysis.

The Pagerank-Index: Going beyond Citation Counts in Quantifying Scientific Impact of Researchers

Quantifying and comparing the scientific output of researchers has become critical for governments, funding agencies and universities. Comparison by reputation and direct assessment of contributions to the field is no longer possible, as the number of scientists increases and traditional definitions about scientific fields become blurred. The h-index is often used for comparing scientists, but has several well-documented shortcomings. In this paper, we introduce a new index for measuring and comparing the publication records of scientists: the pagerank-index (symbolised as π). The index uses a version of pagerank algorithm and the citation networks of papers in its computation, and is fundamentally different from the existing variants of h-index because it considers not only the number of citations but also the actual impact of each citation. We adapt two approaches to demonstrate the utility of the new index. Firstly, we use a simulation model of a community of authors, whereby we create various ‘groups’ of authors which are different from each other in inherent publication habits, to show that the pagerank-index is fairer than the existing indices in three distinct scenarios: (i) when authors try to ‘massage’ their index by publishing papers in low-quality outlets primarily to self-cite other papers (ii) when authors collaborate in large groups in order to obtain more authorships (iii) when authors spend most of their time in producing genuine but low quality publications that would massage their index. Secondly, we undertake two real world case studies: (i) the evolving author community of quantum game theory, as defined by Google Scholar (ii) a snapshot of the high energy physics (HEP) theory research community in arXiv. In both case studies, we find that the list of top authors vary very significantly when h-index and pagerank-index are used for comparison. We show that in both cases, authors who have collaborated in large groups and/or published less impactful papers tend to be comparatively favoured by the h-index, whereas the pagerank-index highlights authors who have made a relatively small number of definitive contributions, or written papers which served to highlight the link between diverse disciplines, or typically worked in smaller groups. Thus, we argue that the pagerank-index is an inherently fairer and more nuanced metric to quantify the publication records of scientists compared to existing measures.

Information-cloning of scale-free networks

In this paper, we introduce a method, Assortative Preferential Attachment, to grow a scale-free network with a given assortativeness value. Utilizing this method, we investigate information-cloning -- recovery of scale-free networks in terms of their information transfer -- and identify a number of recovery features: a full-recovery threshold, a phase transition for both assortative and disassortative networks, and a bell-shaped complexity curve for nonassortative networks. These features are interpreted with respect to two opposing tendencies dominating network recovery: an increasing amount of choice in adding assortative/ disassortative connections, and an increasing divergence between the joint remaining-degree distributions of existing and required networks.

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.

Evolutionary stable strategies in networked games: the influence of topology

Abstract 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.

Node Assortativity in Complex Networks: An Alternative Approach

Abstract Assortativity quantifies the tendency of nodes being connected to similar nodes in a complex network. Degree Assortativity can be quantified as a Pearson correlation. However, it is insufficient to explain assortative or disassortative tendencies of individual nodes or links, which may be contrary to the overall tendency of the network. A number of ‘local’ assortativity measures have been proposed to address this. In this paper we define and analyse an alternative formulation for node assortativity, primarily for undirected networks. The alternative approach is justified by some inherent shortcomings of existing local measures of assortativity. Using this approach, we show that most real world scale-free networks have disassortative hubs, though we can synthesise model networks which have assortative hubs. Highlighting the relationship between assortativity of the hubs and network robustness, we show that real world networks do display assortative hubs in some instances, particularly when high robustness to targeted attacks is a necessity.

Quantifying topological robustness of networks under sustained targeted attacks

In this paper, we introduce a measure to analyse the structural robustness of complex networks, which is specifically applicable in scenarios of targeted, sustained attacks. The measure is based on the changing size of the largest component as the network goes through disintegration. We argue that the measure can be used to quantify and compare the effectiveness of various attack strategies. Applying this measure, we confirm the result that scale-free networks are comparatively less vulnerable to random attacks and more vulnerable to targeted attacks. Then we analyse the robustness of a range of real world networks, and show that most real world networks are least robust to attacks based on betweenness of nodes. We also show that the robustness values of some networks are more sensitive to the attack strategy as compared to others. Furthermore, robustness coefficient computed using two centrality measures may be similar, even when the computational complexities of calculating these centrality measures may be different. Given this disparity, the robustness coefficient introduced potentially plays a key role in choosing attack and defence strategies for real world networks. While the measure is applicable to all types of complex networks, we clearly demonstrate its relevance to social network analysis.

ON CONGRUITY OF NODES AND ASSORTATIVE INFORMATION CONTENT IN COMPLEX NETWORKS

Many distributed systems lend themselves to be modelled as networks, where nodes can have a range of attributes and properties based on which they may be classified. In this paper, we attempt the task of quantifying varying levels of similarity among nodes in a complex network over a period of time. We analyze how this similarity varies as nodes implement their functional logic and node states vary accordingly. We then use information theory to analyze how much Shannon information is conveyed by such a similarity measure, and how such information varies with time. We also propose node congruity as a measure to quantify the contribution of each node to the networks scalar assortativity. Finally, focussing on networks with binary states, we present algorithms (logic functions) which can be implemented in nodes to maximize or minimize scalar assortativity in a given network, and analyze the corresponding tendencies in information content.