The core decomposition of networks: theory, algorithms and applications

Malliaros, Fragkiskos D.; Giatsidis, Christos; Papadopoulos, Apostolos N.; Vazirgiannis, Michalis

doi:10.1007/s00778-019-00587-4

Cited by 93 publications

(35 citation statements)

References 159 publications

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“…Core decompositions are used to study the resilience or robustness of a network [42]. Due to the existence of single entities that captured the majority of all incoming connections, the k-cores had single nodes from 2011-2019.…”

Section: K-core Decompositionmentioning

confidence: 99%

Dissecting bitcoin blockchain: Empirical analysis of bitcoin network (2009–2020)

Nerurkar

Patel²,

Busnel

et al. 2021

Journal of Network and Computer Applications

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Bitcoin system (or Bitcoin) is a peer-to-peer and decentralized payment system that uses cryptocurrency named bitcoins (BTCs) and was released as open-source software in 2009. Unlike fiat currencies, there is no centralized authority or any statutory recognition, backing, or regulation for Bitcoin. All transactions are confirmed for validity by a network of volunteer nodes (miners) and after collective agreement is subsequently recorded into a distributed ledger "Blockchain". Bitcoin platform has attracted both social and anti-social elements. On the one hand, it is social as it ensures the exchange of value, maintaining trust in a cooperative, community-driven manner without the need for a trusted third party. At the same time, it is anti-social as it creates hurdles for law enforcement to trace suspicious transactions due to anonymity and privacy. To understand how the social and anti-social tendencies in the user base of Bitcoin affect its evolution, there is a need to analyze the Bitcoin system as a network. The current paper aims to explore the local topology and geometry of the Bitcoin network during its first decade of existence.

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Section: K-core Decompositionmentioning

confidence: 99%

Dissecting bitcoin blockchain: Empirical analysis of bitcoin network (2009–2020)

Nerurkar

Patel²,

Busnel

et al. 2021

Journal of Network and Computer Applications

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“…A -shell is defined as the set of nodes belonging to the k th core but not to the th core 15 . The -core decomposition has proven to be useful in a variety of domains such as identifying and ranking the most influential spreaders in networks, identifying keywords used for classifying documents, and in assessing the robustness of mutualistic ecosystem and protein networks 16 , 17 .…”

Section: Introductionmentioning

confidence: 99%

Interplay between $$k$$-core and community structure in complex networks

Malvestio

Cardillo

Masuda

2020

Sci Rep

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The organisation of a network in a maximal set of nodes having at least k neighbours within the set, known as $$k$$ k -core decomposition, has been used for studying various phenomena. It has been shown that nodes in the innermost $$k$$ k -shells play a crucial role in contagion processes, emergence of consensus, and resilience of the system. It is known that the $$k$$ k -core decomposition of many empirical networks cannot be explained by the degree of each node alone, or equivalently, random graph models that preserve the degree of each node (i.e., configuration model). Here we study the $$k$$ k -core decomposition of some empirical networks as well as that of some randomised counterparts, and examine the extent to which the $$k$$ k -shell structure of the networks can be accounted for by the community structure. We find that preserving the community structure in the randomisation process is crucial for generating networks whose $$k$$ k -core decomposition is close to the empirical one. We also highlight the existence, in some networks, of a concentration of the nodes in the innermost $$k$$ k -shells into a small number of communities.

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“…The model also provides a framework through which different networks for suggested innovation processes can be described and thus compared. This framework can be further extended using a range of suitable algorthmic techniques [47].…”

Section: Resultsmentioning

confidence: 99%

Problem-driven innovation models for emerging technologies

2020

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As a fundamentally resource-intensive endeavour, healthcare innovation can benefit from a problem-based approach. This kind of methodology needs to define the problem by applying a range of well-established techniques, such as ethnographic research, market analysis, and stakeholder exploration. However, no in-depth investigation has taken place on how these techniques interact and relate to one another. As such, an overarching methodology is needed in order to represent, critically assess, and evolve problem-driven, or needled , innovation approaches. Graph theory provides a useful way by which this can be done. This paper exemplifies how different elements of a problem-first approach to innovation can be graphically represented within a system, in order to provide insights into the processes that support real-world impact for new technologies. By providing a more refined description of the needled innovation methodology, it is hoped that these models can drive a more evidence-based and empirical mindset within the field to ultimately drive valuable innovations with increased efficiency.

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The core decomposition of networks: theory, algorithms and applications

Cited by 93 publications

References 159 publications

Dissecting bitcoin blockchain: Empirical analysis of bitcoin network (2009–2020)

Dissecting bitcoin blockchain: Empirical analysis of bitcoin network (2009–2020)

Interplay between $$k$$-core and community structure in complex networks

Problem-driven innovation models for emerging technologies

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