Dynamic graph clustering combining modularity and smoothness

Görke, Robert; Maillard, Pascal; Schumm, Andrea; Staudt, Christian; Wagner, Dorothea

doi:10.1145/2444016.2444021

Cited by 24 publications

(38 citation statements)

References 23 publications

(24 reference statements)

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“…A trade-off is therefore made between remaining faithful to the current data, but minimising the variation between the current partition and the previous one. Similar approaches can be seen in references [14][15][16][17][18][19][20][21]. In this study, we present a mathematical model that inherits this framework and our analysis focuses on data that is sequential in nature.…”

Section: Introductionmentioning

confidence: 81%

A mathematical programming approach for sequential clustering of dynamic networks

Silva¹,

Bennett

Papageorgiou

et al. 2016

Eur. Phys. J. B

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Abstract.A common analysis performed on dynamic networks is community structure detection, a challenging problem that aims to track the temporal evolution of network modules. An emerging area in this field is evolutionary clustering, where the community structure of a network snapshot is identified by taking into account both its current state as well as previous time points. Based on this concept, we have developed a mixed integer non-linear programming (MINLP) model, SeqMod, that sequentially clusters each snapshot of a dynamic network. The modularity metric is used to determine the quality of community structure of the current snapshot and the historical cost is accounted for by optimising the number of node pairs co-clustered at the previous time point that remain so in the current snapshot partition. Our method is tested on social networks of interactions among high school students, college students and members of the Brazilian Congress. We show that, for an adequate parameter setting, our algorithm detects the classes that these students belong more accurately than partitioning each time step individually or by partitioning the aggregated snapshots. Our method also detects drastic discontinuities in interaction patterns across network snapshots. Finally, we present comparative results with similar community detection methods for time-dependent networks from the literature. Overall, we illustrate the applicability of mathematical programming as a flexible, adaptable and systematic approach for these community detection problems.

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Section: Introductionmentioning

confidence: 81%

A mathematical programming approach for sequential clustering of dynamic networks

Silva¹,

Bennett

Papageorgiou

et al. 2016

Eur. Phys. J. B

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“…An extensively stud- (Goldberg et al, 2011;Ma and Huang, 2013;Miller and Eliassi-Rad, 2009;Takaffoli et al, 2011;Tang et al, 2008;Wang et al, 2008) cond-mat http://arxiv.org (Wang et al, 2008) cit-HepTh/Ph http://arxiv.org (Görke et al, 2013;İlhan andÖgüdücü, 2015;Shang et al, 2014) IMDB http://imdb.com (Goldberg et al, 2011) ied type of dynamic networks is the one that models work related collaborations, such as co-authoring of scientific publications or movie creation. Collaboration networks are extensively used by methods that work on snapshot graphs due to the natural timescale they provide (usually scientific papers -as well as moviescan be referred by their publication year).…”

Section: Collaboration Networkmentioning

confidence: 99%

“…They can also be studied as temporal networks of relations. In Table II (Falkowski et al, 2008;Ferry and Bumgarner, 2012;Pizzuti, 2010, 2014;Li et al, 2011;Shang et al, 2014;Tang et al, 2008;Wang et al, 2008) KIT https://goo.gl/gQqo8l (Görke et al, 2013) Mobile phone - Pizzuti, 2010, 2014;Gong et al, 2012;Guo et al, 2014) Technological Networks. The last class of networks widely adopted to test dynamic algorithms is the technological one.…”

Section: Collaboration Networkmentioning

confidence: 99%

Community Discovery in Dynamic Networks

2018

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Several research studies have shown that Complex Networks modeling real-world phenomena are characterized by striking properties: (i) they are organized according to community structure and (ii) their structure evolves with time. Many researchers have worked on methods that can efficiently unveil substructures in complex networks, giving birth to the field of community discovery. A novel and fascinating problem started capturing researcher interest recently: the identification of evolving communities. Dynamic networks can be used to model the evolution of a system: nodes and edges are mutable and their presence, or absence, deeply impacts the community structure that composes them. This survey aims to present the distinctive features and challenges of dynamic community discovery and propose a classification of published approaches. As a "user manual", this work organizes state of the art methodologies into a taxonomy, based on their rationale, and their specific instantiation. Given a definition of network dynamics, desired community characteristics and analytical needs, this survey will support researchers to identify the set of approaches that best fit their needs. The proposed classification could also help researchers to choose in which direction to orient their future research.lated to the mathematical formalism used to describe them. In Figure 1 are shown four different conceptual Static Edge Weighted Snapshots Temporal Networks Model complexity Temporal impact FIG. 1 Network representations. Moving from static graph to interaction ones the model complexity increases while the grain of the temporal information available decreases (Rossetti, 2015).solutions that gradually introduce the temporal dimension in the network modelling process. At one hand we find the complete atemporal scenario (i.e., a single network snapshot capturing a static glimpse of a dynamic phenomenon): network dynamics can be gradually introduced by adopting labels that weights nodes and edges, thus capturing an aggregate network. Following this approach, weights models the number of occurrence of a given node/edge in a pre-determined observation window: with this little increment in the model complexity, several time-dependent analysis neglected before become possible (i.e., tie strength estimation). Aggregation strategies, however, suffer a severe limitation, they do not capture dynamics. For this reason several works model dynamic phenomena with temporally ordered series of network snapshots. This simple modeling choice allows to efficiently keep track of the perturbations occurring on the network topology. However, while the expressivity of the model is increased, the analytical complexity increases as well. When dealing with network snapshots to perform time-aware mining tasks, two issues need to be addressed: (i) how to keep track of multiple stages of the network life and (ii) how to harmonize the analytical results obtained in a snapshot with the outcome of subsequent ones. Dynamic network partition, as well as aggregation, suffe...

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“…In the work by Riedy and Bader, whenever edges are inserted or deleted, the endpoint vertices of such edges are moved from their communities into singleton communities before restarting their agglomerative algorithm [32]. In the work in [33] by Görke et al, the authors present algorithms to maintain a clustering of a dynamic graph where edges appear as a stream by optimizing modularity while guaranteeing smoother clustering dynamics. Our work falls into this second category of dynamic community detection, except that we deal with local communities, which are described next.…”

Section: Community Detectionmentioning

confidence: 99%

Local Community Detection in Dynamic Graphs Using Personalized Centrality

et al. 2017

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Analyzing massive graphs poses challenges due to the vast amount of data available. Extracting smaller relevant subgraphs allows for further visualization and analysis that would otherwise be too computationally intensive. Furthermore, many real data sets are constantly changing, and require algorithms to update as the graph evolves. This work addresses the topic of local community detection, or seed set expansion, using personalized centrality measures, specifically PageRank and Katz centrality. We present a method to efficiently update local communities in dynamic graphs. By updating the personalized ranking vectors, we can incrementally update the corresponding local community. Applying our methods to real-world graphs, we are able to obtain speedups of up to 60× compared to static recomputation while maintaining an average recall of 0.94 of the highly ranked vertices returned. Next, we investigate how approximations of a centrality vector affect the resulting local community. Specifically, our method guarantees that the vertices returned in the community are the highly ranked vertices from a personalized centrality metric.

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Dynamic graph clustering combining modularity and smoothness

Cited by 24 publications

References 23 publications

A mathematical programming approach for sequential clustering of dynamic networks

A mathematical programming approach for sequential clustering of dynamic networks

Community Discovery in Dynamic Networks

Local Community Detection in Dynamic Graphs Using Personalized Centrality

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