D-cores: Measuring Collaboration of Directed Graphs Based on Degeneracy

Giatsidis, Christos; Thilikos, Dimitrios M.; Vazirgiannis, Michalis

doi:10.1109/icdm.2011.46

Cited by 77 publications

(75 citation statements)

References 29 publications

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“…We measure reputation through the D‐core decomposition (Giatsidis, Thilikos, & Vazirgiannis, ) of the full 2009 network. The D‐core decomposition of a directed network computes a set of ( k , l )‐cores, defined as maximally large subgraphs of the network in which each node has at least an in‐degree of k and an out‐degree of l .…”

Section: Methodsmentioning

confidence: 99%

“…We measure reputation through the D-core decomposition (Giatsidis, Thilikos, & Vazirgiannis, 2013) of the full 2009 network. The D-core decomposition of a directed network computes a set of (k,l)-cores, defined as maximally large subgraphs of the network in which each node has at least an in-degree of k and an out-degree of l. These (k,l)-cores are identified in a pruning algorithm that removes nodes from cores depending on their in-and out-degree, mapping each user to a set of (k,l)-cores, as explained more in detail in Giatsidis et al (2013).…”

Section: Measuring Reputation In Twittermentioning

confidence: 99%

See 1 more Smart Citation

Understanding Popularity, Reputation, and Social Influence in the Twitter Society

García¹,

Mavrodiev²,

Casati³

et al. 2017

Policy & Internet

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The pervasive presence of online media in our society has transferred a significant part of political deliberation to online forums and social networking sites. This article examines popularity, reputation, and social influence on Twitter using large-scale digital traces from 2009 and 2016. We process network information on more than 40 million users, calculating new global measures of reputation that build on the D-core decomposition and the bow-tie structure of the Twitter follower network. We integrate our measurements of popularity, reputation, and social influence to evaluate what keeps users active, what makes them more popular, and what determines their influence. We find that there is a range of values in which the risk of a user becoming inactive grows with popularity and reputation. Popularity in Twitter resembles a proportional growth process that is faster in its strongly connected component, and that can be accelerated by reputation when users are already popular. We find that social influence on Twitter is mainly related to popularity rather than reputation, but that this growth of influence with popularity is sublinear. The explanatory and predictive power of our method shows that global network metrics are better predictors of inactivity and social influence, calling for analyses that go beyond local metrics like the number of followers.

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Section: Methodsmentioning

confidence: 99%

Section: Measuring Reputation In Twittermentioning

confidence: 99%

Understanding Popularity, Reputation, and Social Influence in the Twitter Society

García¹,

Mavrodiev²,

Casati³

et al. 2017

Policy & Internet

View full text Add to dashboard Cite

show abstract

“…Definition 10 ((k, l)-core [75]) Given a directed graph G(V, E) and two non-negative integers k and l, the (k, l)-core is the maximum subgraph C of G such that δ in (C) ≥ k and δ out (C) ≥ l .…”

Section: Directed Graphsmentioning

confidence: 99%

A survey of community search over big graphs

et al. 2019

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With the rapid development of information technologies, various big graphs are prevalent in many real applications (e.g., social media and knowledge bases). An important component of these graphs is the network community. Essentially, a community is a group of vertices which are densely connected internally. Community retrieval can be used in many real applications, such as event organization, friend recommendation, and so on. Consequently, how to efficiently find high-quality communities from big graphs is an important research topic in the era of big data. Recently a large group of research works, called community search, have been proposed. They aim to provide efficient solutions for searching high-quality communities from large networks in real-time. Nevertheless, these works focus on different types of graphs and formulate communities in different manners, and thus it is desirable to have a comprehensive review of these works.In this survey, we conduct a thorough review of existing community search works. Moreover, we analyze

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“…Efficient community detection algorithms have been proposed [20] based on reduction of a graph to its k-core subgraph. Extending the concept of k-core to directed graphs and bringing in in-degrees and out-degrees in its definition, community detection algorithms for networks have been devised and quality evaluation of such communities has been proposed [9].…”

Section: Degeneracymentioning

confidence: 99%

Sparsity measure of a network graph: Gini index

Goswami

Murthy

Das

2018

Information Sciences

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This article examines the application of a popular measure of sparsity, Gini Index, on network graphs. A wide variety of network graphs happen to be sparse. But the index with which sparsity is commonly measured in network graphs is edge density, reflecting the proportion of the sum of the degrees of all nodes in the graph compared to the total possible degrees in the corresponding fully connected graph. Thus edge density is a simple ratio and carries limitations, primarily in terms of the amount of information it takes into account in its definition. In this paper, we have provided a formulation for defining sparsity of a network graph by generalizing the concept of Gini Index and call it sparsity index. A majority of the six properties (viz., Robin Hood, Scaling, Rising Tide, Cloning, Bill Gates and Babies) with which sparsity measures are commonly compared are seen to be satisfied by the proposed index. A comparison between edge density and the sparsity index has been drawn with appropriate examples to highlight the efficacy of the proposed index. It has also been shown theoretically that the two measures follow similar trend for a changing graph, i.e., as the edge density of a graph increases its sparsity index decreases. Additionally, the paper draws a relationship, analytically, between the sparsity index and the exponent term of a power law distribution, a distribution which is known to approximate the degree distribution of a wide variety of network graphs. Finally, the article highlights how the proposed index together with Gini index can reveal important properties of a network graph.

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D-cores: Measuring Collaboration of Directed Graphs Based on Degeneracy

Cited by 77 publications

References 29 publications

Understanding Popularity, Reputation, and Social Influence in the Twitter Society

Understanding Popularity, Reputation, and Social Influence in the Twitter Society

A survey of community search over big graphs

Sparsity measure of a network graph: Gini index

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