Network theory

About: Network theory is a research topic. Over the lifetime, 2257 publications have been published within this topic receiving 109864 citations.

The Accounting Network: How Financial Institutions React to Systemic Crisis.

Abstract: The role of Network Theory in the study of the financial crisis has been widely spotted in the latest years. It has been shown how the network topology and the dynamics running on top of it can trigger the outbreak of large systemic crisis. Following this methodological perspective we introduce here the Accounting Network, i.e. the network we can extract through vector similarities techniques from companies’ financial statements. We build the Accounting Network on a large database of worldwide banks in the period 2001–2013, covering the onset of the global financial crisis of mid-2007. After a careful data cleaning, we apply a quality check in the construction of the network, introducing a parameter (the Quality Ratio) capable of trading off the size of the sample (coverage) and the representativeness of the financial statements (accuracy). We compute several basic network statistics and check, with the Louvain community detection algorithm, for emerging communities of banks. Remarkably enough sensible regional aggregations show up with the Japanese and the US clusters dominating the community structure, although the presence of a geographically mixed community points to a gradual convergence of banks into similar supranational practices. Finally, a Principal Component Analysis procedure reveals the main economic components that influence communities’ heterogeneity. Even using the most basic vector similarity hypotheses on the composition of the financial statements, the signature of the financial crisis clearly arises across the years around 2008. We finally discuss how the Accounting Networks can be improved to reflect the best practices in the financial statement analysis.

K-hop centrality metric for identifying influential spreaders in dynamic large-scale social networks

Abstract: Identifying the most influential spreaders in social networks has many practical applications. The existing methods for the purpose are either too time-consuming for dynamic large-scale networks, such as betweenness centrality, closeness centrality, eigenvector centrality and Katz centrality, or do not consider the network topology, such as degree centrality. To design an effective method to identify the most influential nodes in a network, we propose a novel metric, k-hop centrality which is a generalization of degree centrality. The k-hop index is the summation of the number n(i) of nodes within k-hop distance from the node in question, attenuated by 1/αi, for 1 ≤ i ≤ k (α is the average degree of nodes in the network). It is calculated in a localized manner and is complexity-scalable by adjusting the value of k, thus suitable for dynamically changing, large social networks. We adopt the Susceptible Infected Recovered (SIR) model to evaluate the performance of k-hop centrality over four real datasets of complex networks, and experimental results show that our method outperforms state-of-the-art methods in this field in terms of both infection ratios (spreading influence) and computational complexity. Our work sheds some light on designing efficient spreading strategies for complex networks.

Network topology and mean infection times

Abstract: A fundamental concept of social network analysis is centrality. Many analyses represent the network topology in terms of concept transmission/variation, e.g., influence, social structure, community or other aggregations. Even when the temporal nature of the network is considered, analysis is conducted at discrete points along a continuous temporal scale. Unfortunately, well-studied metrics of centrality do not take varying probabilities into account. The assumption that social and other networks that may be physically stationary, e.g., hard wired, are conceptually static in terms of information diffusion or conceptual aggregation (communities, etc.) can lead to incorrect conclusions. Our findings illustrate, both mathematically and experimentally, that if the notion of network topology is not stationary or fixed in terms of the concept, e.g., groups, belonging, community or other aggregations, centrality should be viewed probabilistically. We show through some surprising examples that study of transmission behavior based solely on a graph’s topological and degree properties is lacking when it comes to modeling network propagation or conceptual (vs. physical) structure.

Foundations of nonlinear network theory : part II: losslessness

Abstract: This paper is the second in a two part series [1] which aims to provide a rigorous foundation in the nonlinear domain for the two energy-based concepts which are fundamental to network theory: passivity and losslessness. We hope to clarify the way they enter into both the state-space and the inputoutput viewpoints. Our definition of losslessness is inspired by that of a "conservative system" in classical mechanics, and we use several examples to compareit with other concepts of losslessness found in the literature. We show in detail how our definition avoids the anomalies and contradictions which many current definitions produce. This concept of losslessness has the desirable property of being preserved under interconnections, and we extend it to one which is representation independent as well. Applied to five common classes of n-ports, it allows us to define explicit criteria for losslessness in terms of the state and output equations. In particular we give a rigorous justification for the various equivalent criteria in the linear case. And we give a canonical network realization for a large class of lossless systems.

Extensions of closeness centrality

Abstract: The concept of vertex centrality has long been studied in order to help understand the structure and dynamics of complex networks. It has found wide applicability in practical as well as theoretical areas. Closeness centrality is one of the fundamental approaches to centrality, but one difficulty with using it is that it degenerates for disconnected graphs. Some alternate versions of closeness centrality have been proposed which rectify this problem. This paper points out that these are not true extensions of closeness centrality in the sense that they do not rank the vertices of connected graphs in the same way that closeness centrality does.