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Showing papers on "Network theory published in 2010"


Book
Olaf Sporns1
01 Oct 2010
TL;DR: Olaf Sporns describes how the integrative nature of brain function can be illuminated from a complex network perspective and describes new links between network anatomy and function and investigates how networks shape complex brain dynamics and enable adaptive neural computation.
Abstract: Over the last decade, the study of complex networks has expanded across diverse scientific fields. Increasingly, science is concerned with the structure, behavior, and evolution of complex systems ranging from cells to ecosystems. Modern network approaches are beginning to reveal fundamental principles of brain architecture and function, and in Networks of the Brain, Olaf Sporns describes how the integrative nature of brain function can be illuminated from a complex network perspective. Highlighting the many emerging points of contact between neuroscience and network science, the book serves to introduce network theory to neuroscientists and neuroscience to those working on theoretical network models. Brain networks span the microscale of individual cells and synapses and the macroscale of cognitive systems and embodied cognition. Sporns emphasizes how networks connect levels of organization in the brain and how they link structure to function. In order to keep the book accessible and focused on the relevance to neuroscience of network approaches, he offers an informal and nonmathematical treatment of the subject. After describing the basic concepts of network theory and the fundamentals of brain connectivity, Sporns discusses how network approaches can reveal principles of brain architecture. He describes new links between network anatomy and function and investigates how networks shape complex brain dynamics and enable adaptive neural computation. The book documents the rapid pace of discovery and innovation while tracing the historical roots of the field. The study of brain connectivity has already opened new avenues of study in neuroscience. Networks of the Brain offers a synthesis of the sciences of complex networks and the brain that will be an essential foundation for future research.

1,567 citations


Book
01 Jan 2010
TL;DR: This paper presents a meta-modelling system that automates the very labor-intensive and therefore time-heavy and therefore expensive and expensive process of manually calculating centrality indices.
Abstract: Fundamentals.- I Elements.- Centrality Indices.- Algorithms for Centrality Indices.- Advanced Centrality Concepts.- II Groups.- Local Density.- Connectivity.- Clustering.- Role Assignments.- Blockmodels.- Network Statistics.- Network Comparison.- Network Models.- Spectral Analysis.- Robustness and Resilience.

617 citations


Journal ArticleDOI
TL;DR: A personalised overview into the areas of network epidemiology that have seen the greatest progress in recent years or have the greatest potential to provide novel insights is provided, focusing on the interplay between network theory and epidemiology.
Abstract: The science of networks has revolutionised research into the dynamics of interacting elements. It could be argued that epidemiology in particular has embraced the potential of network theory more than any other discipline. Here we review the growing body of research concerning the spread of infectious diseases on networks, focusing on the interplay between network theory and epidemiology. The review is split into four main sections, which examine: the types of network relevant to epidemiology; the multitude of ways these networks can be characterised; the statistical methods that can be applied to infer the epidemiological parameters on a realised network; and finally simulation and analytical methods to determine epidemic dynamics on a given network. Given the breadth of areas covered and the ever-expanding number of publications, a comprehensive review of all work is impossible. Instead, we provide a personalised overview into the areas of network epidemiology that have seen the greatest progress in recent years or have the greatest potential to provide novel insights. As such, considerable importance is placed on analytical approaches and statistical methods which are both rapidly expanding fields. Throughout this review we restrict our attention to epidemiological issues.

346 citations


Journal ArticleDOI
16 Aug 2010-PLOS ONE
TL;DR: A new centrality metric called leverage centrality is proposed that considers the extent of connectivity of a node relative to the connectivity of its neighbors and may be able to identify critical nodes that are highly influential within the network.
Abstract: Recent developments in network theory have allowed for the study of the structure and function of the human brain in terms of a network of interconnected components. Among the many nodes that form a network, some play a crucial role and are said to be central within the network structure. Central nodes may be identified via centrality metrics, with degree, betweenness, and eigenvector centrality being three of the most popular measures. Degree identifies the most connected nodes, whereas betweenness centrality identifies those located on the most traveled paths. Eigenvector centrality considers nodes connected to other high degree nodes as highly central. In the work presented here, we propose a new centrality metric called leverage centrality that considers the extent of connectivity of a node relative to the connectivity of its neighbors. The leverage centrality of a node in a network is determined by the extent to which its immediate neighbors rely on that node for information. Although similar in concept, there are essential differences between eigenvector and leverage centrality that are discussed in this manuscript. Degree, betweenness, eigenvector, and leverage centrality were compared using functional brain networks generated from healthy volunteers. Functional cartography was also used to identify neighborhood hubs (nodes with high degree within a network neighborhood). Provincial hubs provide structure within the local community, and connector hubs mediate connections between multiple communities. Leverage proved to yield information that was not captured by degree, betweenness, or eigenvector centrality and was more accurate at identifying neighborhood hubs. We propose that this metric may be able to identify critical nodes that are highly influential within the network.

288 citations


Journal ArticleDOI
TL;DR: This conceptual paper examines the nature of networks and how their analysis can shed light upon the processes of knowledge sharing in destinations as they strive to innovate, and shows how epidemic diffusion models can act as analogies for knowledge communication and transfer within a destination network.
Abstract: Tourism destinations have a necessity to innovate in order to remain competitive in an increasingly global environment. A pre-requisite for innovation is the understanding of how destinations source, share and use knowledge. This conceptual paper examines the nature of networks and how their analysis can shed light upon the processes of knowledge sharing in destinations as they strive to innovate. The paper conceptualizes destinations as networks of connected organizations, both public and private, each of which can be considered as a destination stakeholder. In network theory, they represent the nodes within the system. The paper shows how epidemic diffusion models can act as analogies for knowledge communication and transfer within a destination network. These models can be combined with other approaches to network analysis to shed light on how destination networks operate, and how they can be optimized with policy intervention to deliver innovative and competitive destinations. The paper closes with a ...

282 citations


Bruno Latour1
19 Feb 2010
TL;DR: The Second International Seminar on Network Theory: Network Multidimensionality In The Digital Age as mentioned in this paper was the first to address the problem of network multi-dimensionality in the digital age.
Abstract: Keynote speech for the Second International Seminar On Network Theory: Network Multidimensionality In The Digital Age.

231 citations


Journal ArticleDOI
TL;DR: This paper will attempt to sketch the theoretical background to networking drawing on work in sociology, psychology, and business studies and looking at 4 main theoretical frameworks: constructivism, social capital theory, Durkheimian network theory, and the concept of New Social Movements.
Abstract: In recent years, networking and collaboration have become increasingly popular in education. However, there is at present a lack of attention to the theoretical basis of networking, which could illuminate when and when not to network and under what conditions networks are likely to be successful. In this paper, we will attempt to sketch the theoretical background to networking drawing on work in sociology, psychology, and business studies and looking at 4 main theoretical frameworks: constructivism, social capital theory, Durkheimian network theory, and the concept of New Social Movements. We will also explore differences between networks on a number of factors such as goals, activities, density, spread, and power relations.

199 citations


Journal ArticleDOI
TL;DR: The purpose of this research is to shed light on network-based author keyword analysis by integrating social network analysis and bibliometric analysis on the development of RIS research.
Abstract: Research on regional innovation systems (RIS) has evolved into a widely used analytical framework generating the empirical foundation for innovation policy making. The purpose of this research is to shed light on network-based author keyword analysis by integrating social network analysis and bibliometric analysis on the development of RIS research. A total of 432 papers belonging to 36 countries, 276 research institutes, and comprising 1165 keywords, are retrieved from the Web of Science databases for network construction and analysis. The obtained network in this study is capable of providing visual and quantitative insights into the publication trends or knowledge evolution of RIS. Network actors chosen in this study include country, research institute, first author, and keywords. These constitute four types of networks defined in this study: three research focus parallelship (RFP) networks (RFP-country network, RFP-institute network, RFP-author network) and one keyword co-occurrence (KCO) network.

149 citations


Journal ArticleDOI
TL;DR: In this paper, the authors investigated the statistical signatures of the "credit crunch" financial crisis that unfolded between 2008 and 2009 by combining tools from statistical physics and network theory, and devised measures for the collective behavior of stock prices based on the construction of topologically constrained graphs from cross-correlation matrices.
Abstract: The statistical signatures of the 'credit crunch' financial crisis that unfolded between 2008 and 2009 are investigated by combining tools from statistical physics and network theory. We devise measures for the collective behavior of stock prices based on the construction of topologically constrained graphs from cross-correlation matrices. We test the stability, statistical significance and economic meaningfulness of these graphs. The results show an intriguing trend that highlights a consistently decreasing centrality of the financial sector over the last 10 years.

148 citations


Journal ArticleDOI
TL;DR: In this paper, the authors highlight the potential value of network analysis for conservation biogeography and focus attention on some of the challenges that lie ahead in applying it to conservation problems.
Abstract: Aims To highlight the potential value of network analysis for conservation biogeography and to focus attention on some of the challenges that lie ahead in applying it to conservation problemsLocation GlobalMethods We briefly review existing literature and then focus on five important challenges for the further development of network-based approaches in the fieldResults Our five challenges include (i) understanding cross-scale and cross-level linkages in ecological systems (top–down and bottom–up effects, such as trophic cascades, have been demonstrated in food webs but are poorly understood in nested hierarchies such as reserve networks and stream catchments), (ii) capturing dynamic aspects of ecological systems and networks (with a few exceptions we have little grasp of how important whole-network attributes change as the composition of nodes and links changes), (iii) integrating ecological aspects of network theory with metacommunity frameworks and multiple node functions and roles (can we link the spatial patterns of habitat patches in fragmented landscapes, the parallel networks of interacting species using those patches and community-level interactions as defined by metacommunity theory in a single framework?), (iv) integrating the analysis of social and ecological networks (particularly, can they be analysed as a single interacting system?) and (v) laying an empirical foundation for network analysis in conservation biogeography (this will require a larger data bank of well-studied networks from diverse habitats and systems)Main conclusions Recent research has identified a variety of approaches that we expect to contribute to progress in each of our five challenge areas We anticipate that some of the most exciting outcomes of attempts to meet these challenges will be frameworks that unite areas of research, such as food web analysis and metacommunity theory, that have developed independently

132 citations


Journal ArticleDOI
TL;DR: In this article, a bibliometric study of 116 academic articles published in the major scientific journals in the field of organizational studies between 2000 and 2006 is presented to provide more evidence on the characteristics of the field field of studies of interorganizational cooperation networks in the Brazilian context.
Abstract: The aim of this article is to provide more evidence on the characteristics of the field of studies of inter-organizational cooperation networks in the Brazilian context. The field research was carried out through a bibliometric study of 116 academic articles published in the major scientific journals in the field of organizational studies between 2000 and 2006. The methodological procedures followed the guidelines of the study of Oliver and Ebers (1998). The main results obtained from the bibliometric study were: (1) four theories - strategy, resource dependence, network and institutional - consolidate a predominant conceptual base in the orientation of the studies; (2) the research was mainly carried out by qualitative and cross sectional methods; (3) horizontal networks, material and immaterial antecedent resources, as well as the learning and innovation outcomes, were the main focus of the studies in the Brazilian context; (4) the theories of strategy, resource dependence, transaction, social network and institutional costs are considerably over-represented with regard to their Bonacich centrality; (5) the network theory had a strong level of betweenness centrality among the many theories considered in this study.

Journal ArticleDOI
TL;DR: The main requirements that permit a feasible system-theoretic interpretation of network topology in terms of dynamically invariant phase-space properties are discussed and a rigorous interpretation of the clustering coefficient and the betweenness centrality in Terms of invariant objects is proposed.
Abstract: Recently, different approaches have been proposed for studying basic properties of time series from a complex network perspective. In this work, the corresponding potentials and limitations of networks based on recurrences in phase space are investigated in some detail. We discuss the main requirements that permit a feasible system-theoretic interpretation of network topology in terms of dynamically invariant phase-space properties. Possible artifacts induced by disregarding these requirements are pointed out and systematically studied. Finally, a rigorous interpretation of the clustering coefficient and the betweenness centrality in terms of invariant objects is proposed.

Posted Content
TL;DR: In this paper, a conceptual analysis based on recent developments in service science, S-D logic and network/systems theory is presented, which helps practitioners to better manage service and to enable efficient behaviour within multiple contexts with multiple actors and optimising inter-systemic relations.
Abstract: The purpose of this paper is to combine service science (service science, management and engineering, and SSME) and service dominant (S-D) logic contributions with the network and systems-based theories of many-to-many marketing proposed by Gummesson and the viable system approach (VSA), proposed by Italian researchers and highly diffused in Italy during the 2000s. This paper is a conceptual analysis based on recent developments in service science, S-D logic and network/systems theory. Being grounded in network theory, systems thinking and value co-creation, many-to-many marketing is found to be particularly supportive to both service science and S-D logic. It is also found that VSA, being broad, interdisciplinary and based on systems theory and resource-based theory, and with strong influences from biology, sociology and mechanics, is a key to the interpretation of complex phenomena. Both many-to-many and VSA embrace the whole and the general while still considering the detail and its contextual dependency. Both theories are highly suitable for analysing and designing service systems. The paper helps practitioners to better manage service and to enable efficient behaviour within multiple contexts with multiple actors and optimising inter-systemic relations.


Journal ArticleDOI
TL;DR: This paper constructs the LIS coauthorship network using data from 18 core source LIS journals in China covering 6 years, and identifies some key features of this network: this network is a small-world network, and follows the scale-free character.
Abstract: This paper aims to identify the collaboration pattern and network structure of the coauthorship network of library and information science (LIS) in China. Using data from 18 core source LIS journals in China covering 6 years, we construct the LIS coau- thorship network. We analyze the network from both macro and micro perspectives and identify some key features of this network: this network is a small-world network, and follows the scale-free character. In the micro-level, we calculate each author's centrality values and compare them with citation counts. We find that centrality rankings are highly correlated with citation rankings. We also discuss the limitation of current centrality measures for coauthorship network analysis.

Posted Content
28 Jan 2010
TL;DR: It is shown that the most influential spreaders in a social network do not correspond to the best connected people or to the most central people (high betweenness centrality), and the most efficient spreaders are those located within the core of the network as identified by the k-shell decomposition analysis.
Abstract: Networks portray a multitude of interactions through which people meet, ideas are spread, and infectious diseases propagate within a society. Identifying the most efficient "spreaders" in a network is an important step to optimize the use of available resources and ensure the more efficient spread of information. Here we show that, in contrast to common belief, the most influential spreaders in a social network do not correspond to the best connected people or to the most central people (high betweenness centrality). Instead, we find: (i) The most efficient spreaders are those located within the core of the network as identified by the k-shell decomposition analysis. (ii) When multiple spreaders are considered simultaneously, the distance between them becomes the crucial parameter that determines the extend of the spreading. Furthermore, we find that-- in the case of infections that do not confer immunity on recovered individuals-- the infection persists in the high k-shell layers of the network under conditions where hubs may not be able to preserve the infection. Our analysis provides a plausible route for an optimal design of efficient dissemination strategies.

Journal ArticleDOI
TL;DR: In this paper, a conceptual analysis based on recent developments in service science, S-D logic and network/systems theory is presented, showing that VSA, being broad, interdisciplinary and based on systems theory and resource-based theory, and with strong influences from biology, sociology and mechanics, is a key to the interpretation of complex phenomena.
Abstract: Purpose – The purpose of this paper is to combine service science (service science, management and engineering, and SSME) and service dominant (S‐D) logic contributions with the network and systems‐based theories of many‐to‐many marketing proposed by Gummesson and the viable system approach (VSA), proposed by Italian researchers and highly diffused in Italy during the 2000s.Design/methodology/approach – This paper is a conceptual analysis based on recent developments in service science, S‐D logic and network/systems theory.Findings – Being grounded in network theory, systems thinking and value co‐creation, many‐to‐many marketing is found to be particularly supportive to both service science and S‐D logic. It is also found that VSA, being broad, interdisciplinary and based on systems theory and resource‐based theory, and with strong influences from biology, sociology and mechanics, is a key to the interpretation of complex phenomena. Both many‐to‐many and VSA embrace the whole and the general while still c...

Proceedings ArticleDOI
24 Jul 2010
TL;DR: This work introduces a novel centrality metric for dynamic network analysis that exploits an intuition that in order for one node in a dynamic network to influence another over some period of time, there must exist a path that connects the source and destination nodes through intermediaries at different times.
Abstract: Centrality is an important notion in network analysis and is used to measure the degree to which network structure contributes to the importance of a node in a network. While many different centrality measures exist, most of them apply to static networks. Most networks, on the other hand, are dynamic in nature, evolving over time through the addition or deletion of nodes and edges. A popular approach to analyzing such networks represents them by a static network that aggregates all edges observed over some time period. This approach, however, under or overestimates centrality of some nodes. We address this problem by introducing a novel centrality metric for dynamic network analysis. This metric exploits an intuition that in order for one node in a dynamic network to influence another over some period of time, there must exist a path that connects the source and destination nodes through intermediaries at different times. We demonstrate on an example network that the proposed metric leads to a very different ranking than analysis of an equivalent static network. We use dynamic centrality to study a dynamic citations network and contrast results to those reached by static network analysis.

Journal ArticleDOI
TL;DR: In this article, the authors present an in-depth longitudinal case study of a small entrepreneurial firm within the mobile-commerce industry and find that network relationships formed during the earliest stages of the firm's life cycle played a critical role in developing the SME's capacity for sustained innovation.
Abstract: Networks can offer SMEs a number of advantages, especially in terms of providing greater opportunities for knowledge activities that support innovation, but there is little in the literature to suggest how firms develop their innovation capacity through network participation. In this paper, we present an in-depth longitudinal case study of a small entrepreneurial firm within the mobile-commerce industry. A principal finding from the study is that network relationships formed during the earliest stages of the firm’s life cycle played a critical role in developing the SME’s capacity for sustained innovation. Further, the study contributes to network theory by calling into question the weak and strong tie dichotomy, as relationships critical to the SME’s innovation capacity possessed characteristics of both types of ties. The paper also contributes to managerial practice by emphasizing the importance of establishing strong relationships in the earliest stages of network formation.

Journal ArticleDOI
TL;DR: It is shown here that the use of centrality indices based on the zooming in strategy identifies a larger number of essential proteins in the yeast PPI network than any of the other centrality measures studied.

Journal ArticleDOI
TL;DR: A literature-based framework based on innovation network theory and complemented with C–K theory is proposed in order to analyze the invention/innovation process of inventors and the product concepts in a packaging industry context.

Journal ArticleDOI
TL;DR: The search for a systems‐level picture of metabolism as a web of molecular interactions provides a paradigmatic example of how the methods used to characterize a system can bias the interpretation of its functional meaning.
Abstract: The search for a systems-level picture of metabolism as a web of molecular interactions provides a paradigmatic example of how the methods used to characterize a system can bias the interpretation of its functional meaning Metabolic maps have been analyzed using novel techniques from network theory, revealing some non-trivial, functionally relevant properties These include a small-world structure and hierarchical modularity However, as discussed here, some of these properties might actually result from an inappropriate way of defining network interactions Starting from the so-called bipartite organization of metabolism, where the two meaningful subsets (reactions and metabolites) are considered, most current works use only one of the subsets by means of so-called graph projections Unfortunately, projected graphs often ignore relevant biological and chemical constraints, thus leading to statistical artifacts Some of these drawbacks and alternative approaches need to be properly addressed

Journal ArticleDOI
TL;DR: A multiscale decomposition of shortest paths shows that the contributions to betweenness coming from geodesics not longer than L obey a characteristic scaling versus L, which can be used to predict the distribution of the full centralities.
Abstract: Betweenness centrality lies at the core of both transport and structural vulnerability properties of complex networks; however, it is computationally costly, and its measurement for networks with millions of nodes is nearly impossible. By introducing a multiscale decomposition of shortest paths, we show that the contributions to betweenness coming from geodesics not longer than L obey a characteristic scaling versus L, which can be used to predict the distribution of the full centralities. The method is also illustrated on a real-world social network of 5.5 × 10(6) nodes and 2.7 × 10(7) links.

Journal IssueDOI
TL;DR: The topological centrality measure reflecting the topological positions of node and edges as well as influence between nodes and edges in general network is proposed.
Abstract: Network structure analysis plays an important role in characterizing complex systems. Different from previous network centrality measures, this article proposes the topological centrality measure reflecting the topological positions of nodes and edges as well as influence between nodes and edges in general network. Experiments on different networks show distinguished features of the topological centrality by comparing with the degree centrality, closeness centrality, betweenness centrality, information centrality, and PageRank. The topological centrality measure is then applied to discover communities and to construct the backbone network. Its characteristics and significance is further shown in e-Science applications. © 2010 Wiley Periodicals, Inc.

Journal ArticleDOI
TL;DR: In this article, centrality of an edge is defined as a degree of global sensitivity of a graph distance function (i.e., a graph metric) on the weight of the considered edge.
Abstract: Centrality of an edge of a graph is proposed to be viewed as a degree of global sensitivity of a graph distance function (i.e., a graph metric) on the weight of the considered edge. For different choices of distance function, contact is made with several previous ideas of centrality, whence their different characteristics are clarified, and strengths or short-comings are indicated, via selected examples. The centrality based on “resistance distance” exhibits several nice features, and might be termed “amongness” centrality.

Journal ArticleDOI
TL;DR: A new measure of vulnerability of a node in a complex network is proposed based on the analogy in which the nodes of the network are represented by balls and the links are identified with springs, which suggests that the node displacement has a better resolution of the vulnerability than the information centrality.
Abstract: We propose a new measure of vulnerability of a node in a complex network. The measure is based on the analogy in which the nodes of the network are represented by balls and the links are identified with springs. We define the measure as the node displacement, or the amplitude of vibration of each node, under fluctuation due to the thermal bath in which the network is supposed to be submerged. We prove exact relations among the thus defined node displacement, the information centrality and the Kirchhoff index. The relation between the first two suggests that the node displacement has a better resolution of the vulnerability than the information centrality, because the latter is the sum of the local node displacement and the node displacement averaged over the entire network.

Journal ArticleDOI
TL;DR: This work determines the qualitative and quantitative conditions by which dispersal and network structure control the persistence of a set of age-structured patch populations and reveals new insights regarding the determinants of persistence, stability, and thresholds in complex metapopulations.
Abstract: Synthesising the relationships between complexity, connectivity, and the stability of large biological systems has been a longstanding fundamental quest in theoretical biology and ecology. With the many exciting developments in modern network theory, interest in these issues has recently come to the forefront in a range of multidisciplinary areas. Here we outline a new theoretical analysis specifically relevant for the study of ecological metapopulations focusing primarily on marine systems, where subpopulations are generally connected via larval dispersal. Our work determines the qualitative and quantitative conditions by which dispersal and network structure control the persistence of a set of age-structured patch populations. Mathematical modelling combined with a graph theoretic analysis demonstrates that persistence depends crucially on the topology of cycles in the dispersal network which tend to enhance the effect of larvae “returning home.” Our method clarifies the impact directly due to network structure, but this almost by definition can only be achieved by examining the simplified case in which patches are identical; an assumption that we later relax. The methodology identifies critical migration routes, whose presence are vital to overall stability, and therefore should have high conservation priority. In contrast, “lonely links,” or links in the network that do not participate in a cyclical component, have no impact on persistence and thus have low conservation priority. A number of other intriguing criteria for persistence are derived. Our modelling framework reveals new insights regarding the determinants of persistence, stability, and thresholds in complex metapopulations. In particular, while theoretical arguments have, in the past, suggested that increasing connectivity is a destabilizing feature in complex systems, this is not evident in metapopulation networks where connectivity, cycles, coherency, and heterogeneity all tend to enhance persistence. The results should be of interest for many other scientific contexts that make use of network theory.

Journal ArticleDOI
TL;DR: In this article, the authors examined the impact of a firm's innovation by analyzing its position in a global research and development network and its orientation toward using scientific knowledge (science intensity).
Abstract: The authors examine the impact of a firm's innovation by analyzing its position in a global research-and-development network and its orientation toward using scientific knowledge (science intensity). Drawing on organizational learning and network theory research, they focus on the moderating role of a firm's network position in the relationship between the firm's science intensity and the impact of its innovation. Data derived from the global pharmaceutical industry indicate that a firm's science intensity enhances the impact of its innovation by facilitating effective search. This relationship is reinforced when the firm has network resources derived from an efficient network position. These results support the idea that the impact of innovation is strengthened when internal research capability and external network resources are combined. This study, which is conducted in a global industry network context, also enables the authors to examine the role of international gatekeepers in bridging ties...

Journal ArticleDOI
20 Jun 2010-Symmetry
TL;DR: In this paper, the authors established various connections between complex networks and symmetry and proposed a definition of stochastic symmetry based on graph ensembles and use it to review the main results of network theory from an unusual perspective.
Abstract: In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs, the analysis of more general symmetries in real complex networks is far less developed. We argue that real networks, as any entity characterized by imperfections or errors, necessarily require a stochastic notion of invariance. We therefore propose a definition of stochastic symmetry based on graph ensembles and use it to review the main results of network theory from an unusual perspective. The results discussed here and in a companion paper show that stochastic symmetry highlights the most informative topological properties of real networks, even in noisy situations unaccessible to exact techniques.

Journal ArticleDOI
TL;DR: The aim of this article is to investigate the governance models of companies listed on the Italian Stock Exchange by using a network approach, which describes the interlinks between boards of directors using a weighted graph representing the listed companies and their relationships.
Abstract: The aim of this article is to investigate the governance models of companies listed on the Italian Stock Exchange by using a network approach, which describes the interlinks between boards of directors. Following mainstream literature, I construct a weighted graph representing the listed companies (vertices) and their relationships (weighted edges), the Corporate Board Network; I then apply three different vertex centrality measures: degree, betweenness and flow betweenness. What emerges from the network construction and by applying the degree centrality is a structure with a large number of connections but not particularly dense, where the presence of a small number of highly connected nodes (hubs) is evident. Then I focus on betweenness and flow betweenness; indeed I expect that these centrality measures may give a representation of the intensity of the relationship between companies, capturing the volume of information flowing from one vertex to another. Finally, I investigate the possible scale-free structure of the network.