Graph Clustering and Minimum Cut Trees

Flake, Gary William; Tarjan, Robert E.; Tsioutsiouliklis, Kostas

doi:10.1080/15427951.2004.10129093

Cited by 255 publications

(196 citation statements)

References 21 publications

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“…In the web context, a community is defined by Flake et al [31] as a set of web pages that links to more web pages in the community than to pages out of community. Interesting weighted extensions are studied in [32]. The problem of partitioning into communities, so as to identify clusters, amounts to determining a satisfactory k-partition, for a given or suitably chosen k.…”

Section: Applications and Related Problemsmentioning

confidence: 99%

Satisfactory graph partition, variants, and generalizations

Bazgan

Tuza

Vanderpooten

2010

European Journal of Operational Research

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Section: Applications and Related Problemsmentioning

confidence: 99%

Satisfactory graph partition, variants, and generalizations

Bazgan

Tuza

Vanderpooten

2010

European Journal of Operational Research

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“…Very relevant to our work is that of Kannan, Vempala, and Vetta [93], who analyze spectral algorithms and describe a community concept in terms of a bicriterion depending on the conductance of the communities and the relative weight of inter-community edges. Flake, Tarjan, and Tsioutsiouliklis [69] introduce a similar bicriterion that is based on network flow ideas, and Flake et al [67,68] defined a community as a set of nodes that has more intra-edges than inter-edges. Similar edge-counting ideas were used by Radicchi et al [136] to define and apply the notions of a strong community and a weak community.…”

Section: Relationship With Community Identification Methodsmentioning

confidence: 99%

Community Structure in Large Networks: Natural Cluster Sizes and the Absence of Large Well-Defined Clusters

Leskovec¹,

Lang²,

Dasgupta³

et al. 2009

Internet Mathematics

1,496

1,082

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A large body of work has been devoted to defining and identifying clusters or communities in social and information networks, i.e., in graphs in which the nodes represent underlying social entities and the edges represent some sort of interaction between pairs of nodes. Most such research begins with the premise that a community or a cluster should be thought of as a set of nodes that has more and/or better connections between its members than to the remainder of the network. In this paper, we explore from a novel perspective several questions related to identifying meaningful communities in large social and information networks, and we come to several striking conclusions.Rather than defining a procedure to extract sets of nodes from a graph and then attempt to interpret these sets as a "real" communities, we employ approximation algorithms for the graph partitioning problem to characterize as a function of size the statistical and structural properties of partitions of graphs that could plausibly be interpreted as communities. In particular, we define the network community profile plot, which characterizes the "best" possible community-according to the conductance measure-over a wide range of size scales. We study over 100 large real-world networks, ranging from traditional and on-line social networks, to technological and information networks and web graphs, and ranging in size from thousands up to tens of millions of nodes.Our results suggest a significantly more refined picture of community structure in large networks than has been appreciated previously. Our observations agree with previous work on small networks, but we show that large networks have a very different structure. In particular, we observe tight communities that are barely connected to the rest of the network at very small size scales (up to ≈ 100 nodes); and communities of size scale beyond ≈ 100 nodes gradually "blend into" the expanderlike core of the network and thus become less "community-like," with a roughly inverse relationship between community size and optimal community quality. This observation agrees well with the so-called Dunbar number which gives a limit to the size of a well-functioning community.However, this behavior is not explained, even at a qualitative level, by any of the commonly-used network generation models. Moreover, it is exactly the opposite of what one would expect based on intuition from expander graphs, low-dimensional or manifold-like graphs, and from small social networks that have served as testbeds of community detection algorithms. The relatively gradual increase of the network community profile plot as a function of increasing community size depends in a subtle manner on the way in which local clustering information is propagated from smaller to larger size scales in the network. We have found that a generative graph model, in which new edges are added via an iterative "forest fire" burning process, is able to produce graphs exhibiting a network community profile plot similar to what we observe i...

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“…It provides strong connectedness within the cluster" [11]. Min-cut based clustering algorithm [11] is given in Table 2.…”

Section: Graph Based Modellingmentioning

confidence: 99%

“…It provides strong connectedness within the cluster" [11]. Min-cut based clustering algorithm [11] is given in Table 2. As specified in [11] number of clusters created depends on the value of α.…”

Section: Graph Based Modellingmentioning

confidence: 99%