Triadic closure in two-mode networks: Redefining the global and local clustering coefficients
TL;DR: This paper proposes redefinitions of the clustering coefficients for two-mode networks, which are proposed to overcome issues arise in this transformation process, especially when analyzing ties among nodes’ contacts.
About: This article is published in Social Networks.The article was published on 2013-05-01 and is currently open access. It has received 423 citations till now. The article focuses on the topics: Evolving networks & Clustering coefficient.
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TL;DR: A complete overview of the emerging field of networks beyond pairwise interactions, and focuses on novel emergent phenomena characterizing landmark dynamical processes, such as diffusion, spreading, synchronization and games, when extended beyond Pairwise interactions.
740 citations
Cites background from "Triadic closure in two-mode network..."
...The global clustering coefficient can however be defined through its one-mode projections, as the number of 4-paths in the bipartite graph that are part of a 6-cycle [112, 113]....
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TL;DR: It is shown that there is a rich variety of structure in the authors' datasets but datasets from the same system types have consistent patterns of higher-order structure, and it is found that tie strength and edge density are competing positive indicators ofhigher-order organization.
Abstract: Networks provide a powerful formalism for modeling complex systems by using a model of pairwise interactions. But much of the structure within these systems involves interactions that take place among more than two nodes at once-for example, communication within a group rather than person to person, collaboration among a team rather than a pair of coauthors, or biological interaction between a set of molecules rather than just two. Such higher-order interactions are ubiquitous, but their empirical study has received limited attention, and little is known about possible organizational principles of such structures. Here we study the temporal evolution of 19 datasets with explicit accounting for higher-order interactions. We show that there is a rich variety of structure in our datasets but datasets from the same system types have consistent patterns of higher-order structure. Furthermore, we find that tie strength and edge density are competing positive indicators of higher-order organization, and these trends are consistent across interactions involving differing numbers of nodes. To systematically further the study of theories for such higher-order structures, we propose higher-order link prediction as a benchmark problem to assess models and algorithms that predict higher-order structure. We find a fundamental difference from traditional pairwise link prediction, with a greater role for local rather than long-range information in predicting the appearance of new interactions.
361 citations
Cites background from "Triadic closure in two-mode network..."
...Prior research has also identified the distinction between open and closed triangles when projecting bipartite networks but has not studied the idea of simplicial closure events (7, 48)....
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TL;DR: In this article, the authors measure the complexity of knowledge, map the distribution and the evolution of knowledge complexity in US cities, and explore how the spatial diffusion of knowledge is linked to complexity.
Abstract: There is consensus among scholars and policy makers that knowledge is one of the key drivers of long-run economic growth. It is also clear from the literature that not all knowledge has the same value. However, too often in economic geography and cognate fields we have been obsessed with counting knowledge inputs and outputs rather than assessing the quality of knowledge produced. In this article we measure the complexity of knowledge, we map the distribution and the evolution of knowledge complexity in US cities, and we explore how the spatial diffusion of knowledge is linked to complexity. Our knowledge complexity index rests on the bimodal network models of Hidalgo and Hausmann. Analysis is based on more than two million patent records from the US Patent and Trademark Office that identify the technological structure of US metropolitan areas in terms of the patent classes in which they are most active between 1975 and 2010. We find that knowledge complexity is unevenly distributed across the Uni...
282 citations
Cites background from "Triadic closure in two-mode network..."
...This type of network is also referred to as a bipartite, bimodal, or an affiliation network in the network science literature (Opsahl 2013)....
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TL;DR: This work introduces a novel method, based on persistent homology, to detect particular non-local structures, akin to weighted holes within the link-weight network fabric, which are invisible to existing methods and creates the first bridge between network theory and algebraic topology, which will allow to import the toolset of algebraic methods to complex systems.
Abstract: The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally defined quantities of nodes and edges, such as node degrees, edge weights and –more recently– correlations between neighboring nodes. However, statistical methods quickly become cumbersome when dealing with many-body properties and do not capture the precise mesoscopic structure of complex networks. Here we introduce a novel method, based on persistent homology, to detect particular non-local structures, akin to weighted holes within the link-weight network fabric, which are invisible to existing methods. Their properties divide weighted networks in two broad classes: one is characterized by small hierarchically nested holes, while the second displays larger and longer living inhomogeneities. These classes cannot be reduced to known local or quasilocal network properties, because of the intrinsic non-locality of homological properties, and thus yield a new classification built on high order coordination patterns. Our results show that topology can provide novel insights relevant for many-body interactions in social and spatial networks. Moreover, this new method creates the first bridge between network theory and algebraic topology, which will allow to import the toolset of algebraic methods to complex systems.
232 citations
Cites background from "Triadic closure in two-mode network..."
...The online forum network refers to the same online community, but focuses on the activity of users in public forums, rather than on private messages [42]....
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Book•
18 Jul 2016TL;DR: This book unifies and consolidates existing practical and theoretical knowledge on multilayer networks including data collection and analysis, modeling, and mining of multilayers social network systems, the evolution of interconnected social networks, and dynamic processes such as information spreading.
Abstract: Multilayer networks, in particular multilayer social networks, where users belong to and interact on different networks at the same time, are an active research area in social network analysis, computer science, and physics. These networks have traditionally been studied within these separate research communities, leading to the development of several independent models and methods to deal with the same set of problems. This book unifies and consolidates existing practical and theoretical knowledge on multilayer networks including data collection and analysis, modeling, and mining of multilayer social network systems, the evolution of interconnected social networks, and dynamic processes such as information spreading. A single real dataset is used to illustrate the concepts presented throughout the book, demonstrating both the practical utility and the potential shortcomings of the various methods. Researchers from all areas of network analysis will learn new aspects and future directions of this emerging field.
163 citations
References
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TL;DR: Simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder are explored, finding that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs.
Abstract: Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games, genetic control networks and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks 'rewired' to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them 'small-world' networks, by analogy with the small-world phenomenon (popularly known as six degrees of separation. The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices.
39,297 citations
TL;DR: In this paper, it is argued that the degree of overlap of two individuals' friendship networks varies directly with the strength of their tie to one another, and the impact of this principle on diffusion of influence and information, mobility opportunity, and community organization is explored.
Abstract: Analysis of social networks is suggested as a tool for linking micro and macro levels of sociological theory. The procedure is illustrated by elaboration of the macro implications of one aspect of small-scale interaction: the strength of dyadic ties. It is argued that the degree of overlap of two individuals' friendship networks varies directly with the strength of their tie to one another. The impact of this principle on diffusion of influence and information, mobility opportunity, and community organization is explored. Stress is laid on the cohesive power of weak ties. Most network models deal, implicitly, with strong ties, thus confining their applicability to small, well-defined groups. Emphasis on weak ties lends itself to discussion of relations between groups and to analysis of segments of social structure not easily defined in terms of primary groups.
37,560 citations
TL;DR: In this paper, the concept of social capital is introduced and illustrated, its forms are described, the social structural conditions under which it arises are examined, and it is used in an analys...
Abstract: In this paper, the concept of social capital is introduced and illustrated, its forms are described, the social structural conditions under which it arises are examined, and it is used in an analys...
31,693 citations
Book•
25 Nov 1994TL;DR: This paper presents mathematical representation of social networks in the social and behavioral sciences through the lens of Dyadic and Triadic Interaction Models, which describes the relationships between actor and group measures and the structure of networks.
Abstract: Part I. Introduction: Networks, Relations, and Structure: 1. Relations and networks in the social and behavioral sciences 2. Social network data: collection and application Part II. Mathematical Representations of Social Networks: 3. Notation 4. Graphs and matrixes Part III. Structural and Locational Properties: 5. Centrality, prestige, and related actor and group measures 6. Structural balance, clusterability, and transitivity 7. Cohesive subgroups 8. Affiliations, co-memberships, and overlapping subgroups Part IV. Roles and Positions: 9. Structural equivalence 10. Blockmodels 11. Relational algebras 12. Network positions and roles Part V. Dyadic and Triadic Methods: 13. Dyads 14. Triads Part VI. Statistical Dyadic Interaction Models: 15. Statistical analysis of single relational networks 16. Stochastic blockmodels and goodness-of-fit indices Part VII. Epilogue: 17. Future directions.
17,104 citations