Zur allgemeinen Kurventheorie

Menger, Karl

doi:10.4064/fm-10-1-96-115

Cited by 1,023 publications

(470 citation statements)

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“…A graph G is k-connected if its connectivity is at least k. It is k-edge-connected when its edge connectivity is at least k. Karl Menger (1927) proved the equality of k-connectedness and the minimum number of node-independent paths between every pair of nodes, 23 which is a property of how a graph can be traversed. Consider graph G 1 in Figure 7: There is no pair of nodes with fewer than two node-independent paths, such as join nodes 1 and 2.…”

Section: D+ Connectivity and Multiple Independent Paths As Cohesion mentioning

confidence: 99%

“…This allows us to equate the sociological definitions 1.1.2 and 1.2.2 for cohesion and 2.1.2 and 2.2.2 for adhesion with corresponding graph theoretic definitions of node and edge connectivity and, using the theorems of Menger (1927), to establish the equality between the two fundamental properties of cohesion and adhesion: resistance to being pulled apart (definitions 1.1.2 and 2.1.2), and stick-togetherness (1.2.2 and 2.2.2). Our goal in this section is to provide a formal methodology with appropriate graph theoretic terminology for the cohesive (or adhesive) blocking of social networks.…”

Section: The Graph Theoretic Foundations Of Cohesion and Adhesionmentioning

confidence: 99%

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The Cohesiveness of Blocks In Social Networks: Node Connectivity and Conditional Density

White

Harary

2001

Sociological Methodology

238

166

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Section: D+ Connectivity and Multiple Independent Paths As Cohesion mentioning

confidence: 99%

Section: The Graph Theoretic Foundations Of Cohesion and Adhesionmentioning

confidence: 99%

The Cohesiveness of Blocks In Social Networks: Node Connectivity and Conditional Density

White

Harary

2001

Sociological Methodology

238

166

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“…While the crucial mathematical concept for emergent cohesive subsets in networks was discovered by Menger (1927), a central element missing in most social and natural science network studies has been an adequate theoretical conception and measurement of the concept, which we term structural cohesion (Moody and White, 2003). Structural cohesion has two distinct but deeply equivalent facets.…”

Section: From Embeddedness To Cohesionmentioning

confidence: 99%

Networks, Fields and Organizations: Micro-Dynamics, Scale and Cohesive Embeddings

White

Owen‐Smith

Moody

et al. 2004

Computational & Mathematical Organization Theory

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Social action is situated in fields that are simultaneously composed of interpersonal ties and relations among organizations, which are both usefully characterized as social networks. We introduce a novel approach to distinguishing different network macro-structures in terms of cohesive subsets and their overlaps. We develop a vocabulary that relates different forms of network cohesion to field properties as opposed to organizational constraints on ties and structures. We illustrate differences in probabilistic attachment processes in network evolution that link on the one hand to organizational constraints versus field properties and to cohesive network topologies on the other. This allows us to identify a set of important new micro-macro linkages between local behavior in networks and global network properties. The analytic strategy thus puts in place a methodology for Predictive Social Cohesion theory to be developed and tested in the context of informal and formal organizations and organizational fields. We also show how organizations and fields combine at different scales of cohesive depth and cohesive breadth. Operational measures and results are illustrated for three organizational examples, and analysis of these cases suggests that different structures of cohesive subsets and overlaps may be predictive in organizational contexts and similarly for the larger fields in which they are embedded. Useful predictions may also be based on feedback from level of cohesion in the larger field back to organizations, conditioned on the level of multiconnectivity to the field.

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“…We modify the social network graph by creating a new node s and connecting it to every one of the initially trusted nodes. According to Menger's theorem [11], s and v are not separated by a vertex cut of size at most k if and only if there exist at least k + 1 vertex-disjoint paths between s and v. The lemma follows immediately.…”

Section: There Exist K + 1 Vertex-disjoint Paths From (Distinct) Initmentioning

confidence: 59%

False-Name-Proofness in Social Networks

Conitzer

Immorlica²,

Letchford

et al. 2010

Lecture Notes in Computer Science

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In mechanism design, the goal is to create rules for making a decision based on the preferences of multiple parties (agents), while taking into account that agents may behave strategically. An emerging phenomenon is to run such mechanisms on a social network; for example, Facebook recently allowed its users to vote on its future terms of use. One significant complication for such mechanisms is that it may be possible for a user to participate multiple times by creating multiple identities. Prior work has investigated the design of false-name-proof mechanisms, which guarantee that there is no incentive to use additional identifiers. Arguably, this work has produced mostly negative results. In this paper, we show that it is in fact possible to create good mechanisms that are robust to false-name-manipulation, by taking the social network structure into account. The basic idea is to exclude agents that are separated from trusted nodes by small vertex cuts. We provide key results on the correctness, optimality, and computational tractability of this approach.

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Zur allgemeinen Kurventheorie

Cited by 1,023 publications

References 0 publications

The Cohesiveness of Blocks In Social Networks: Node Connectivity and Conditional Density

The Cohesiveness of Blocks In Social Networks: Node Connectivity and Conditional Density

Networks, Fields and Organizations: Micro-Dynamics, Scale and Cohesive Embeddings

False-Name-Proofness in Social Networks

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