Weighted Graph Cuts without Eigenvectors A Multilevel Approach

Dhillon, Inderjit S.; Guan, Yuqiang; Kulis, Brian

doi:10.1109/tpami.2007.1115

Cited by 876 publications

(624 citation statements)

References 20 publications

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“…Conductance is widely used to capture the intuition of a good community; it is a fundamental combinatorial quantity; and it has a very natural interpretation in terms of random walks on the interaction graph. Moreover, since there exist a rich suite of both theoretical and practical algorithms [87,149,107,108,17,95,96,162,54], we can for point (4) compare and contrast several methods to approximately optimize it. To illustrate conductance, note that of the three 5-node sets A, B, and C illustrated in the graph in Figure 1, B has the best (the lowest) conductance and is thus the most community-like.…”

Section: Overview Of Our Approachmentioning

confidence: 99%

See 1 more Smart Citation

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

Leskovec¹,

Lang²,

Dasgupta³

et al. 2009

Internet Mathematics

1,512

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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Section: Overview Of Our Approachmentioning

confidence: 99%

“…We have tried a number of them, including Graclus [54] and Newman's modularity optimizing program (we refer to it as Dendrogram) [80]. Graclus attempts to find a partitioning of a graph into pieces bounded by low-conductance cuts using a kernel k-means algorithm.…”

Section: Leighton-rao: Connected Clusters (Green) Disconnected Clustmentioning

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

1,512

1,082

View full text Add to dashboard Cite

show abstract

“…Such a subgroup is also called as a cluster in a graph. By applying graph clustering algorithms such as Graclus [9] or GEM [10] for larger networks, we can partition a given graph into a set of clusters. Formally, given a graph G = (V, E), a set of k clusters for the graph can be represented as…”

Section: Graph Partitioningmentioning

confidence: 99%

Localized Ranking in Social and Information Networks

Whang

Shin

2018

IEICE Trans. Inf. & Syst.

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SUMMARYIn social and information network analysis, ranking has been considered to be one of the most fundamental and important tasks where the goal is to rank the nodes of a given graph according to their importance. For example, the PageRank and the HITS algorithms are wellknown ranking methods. While these traditional ranking methods focus only on the structure of the entire network, we propose to incorporate a local view into node ranking by exploiting the clustering structure of realworld networks. We develop localized ranking mechanisms by partitioning the graphs into a set of tightly-knit groups and extracting each of the groups where the localized ranking is computed. Experimental results show that our localized ranking methods rank the nodes quite differently from the traditional global ranking methods, which indicates that our methods provide new insights and meaningful viewpoints for network analysis.

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“…Hence, partitioning a graph by minimizing the normalized cut (a modification of cut) [58] identifies communities with strong internal connections that are weakly linked to each other by low weight edges. Several algorithms are available for this purpose [58][59][60][61][62]. However, most of them require the number of desired communities as input.…”

Section: Decomposition Of Weighted Contact Graph Into Communitiesmentioning

confidence: 99%

Routing in Opportunistic Networks

Woungang¹,

Dhurandher²,

Anpalagan³

et al. 2013

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Opportunistic networking is employed in scenarios where end-to-end communication paths between nodes cannot be assumed due to continuously changing network topology. In these networks, data is routed in a "store-carry-forward" fashion by exploiting the transient communication opportunities that arise when mobile nodes equipped with short-range wireless interfaces come within each other's transmission range. Designing efficient routing schemes for opportunistic networks is challenging as they face a trade-off between delivery performance and resource consumption. In this thesis, we propose a novel opportunistic routing algorithm that addresses this trade-off by incorporating information about the node contact pattern in the network. Aggregating contact events into a weighted graph enables us to detect communities and learn about the neighbourhoods of nodes. This information is utilized by our algorithm to assess the usefulness of every forwarding opportunity that arises. Performance evaluation of the proposed algorithm shows that it is capable of achieving good delivery performance while consuming significantly fewer resources in comparison to the existing opportunistic routing algorithms.ii Sommaire Le réseautage opportuniste est utilisé dans les scénarios où l'existence de routes de communication entre agents ne peut pasêtre présumé dûà l'altération constante de la topologie du réseau. Dans ces réseaux, l'information est acheminée grâceà une procédure de "sauvegarde-report" qui exploite les opportunités de communication transitoires qui ont lieu lorsque des agentséquippés d'interface sans-filà petite portée entrent dans leurs périmètres de portée respectifs.Établir des plans de communication efficaces dans le contexte de réseaux opportunistes est un défi puisque ceux-ci font faceà un compromis entre performance de livraison et consommation de ressources. Dans cette thèse, nous proposons un algorithme de routage opportuniste original qui addresse ce compromis en incorporant l'information liée aux contacts entre noeuds du réseau. Assembler lesévènements de contacts dans un graphe pondéré nous permet de détecter les communautés et d'apprendre le voisinage de chaque noeud. Cette information est utilisée par notre algorithme afin d'évaluer l'utilité de chaque opportunité de communication qui se présente. Une analyse de la performance de l'algorithme proposé montre qu'il est capable d'atteindre une bonne performance de livraison tout en consommant significativement moins de ressources lorsque comparé aux algorithmes de routage opportuniste actuels.iii

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Weighted Graph Cuts without Eigenvectors A Multilevel Approach

Cited by 876 publications

References 20 publications

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

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

Localized Ranking in Social and Information Networks

Routing in Opportunistic Networks

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