Limited resolution in complex network community detection with Potts model approach

Kumpula, Jussi M.; Saramäki, Jari; Kaski, Kimmo; Kertész, János

doi:10.1140/epjb/e2007-00088-4

Cited by 152 publications

(160 citation statements)

References 22 publications

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“…We use a random rewiring of the original graph to sample G(G ) (Maslov & Sneppen 2002), and the heuristics proposed in Newman (2006) to calculateQ. We note that it is notoriously difficult to compare modularity of networks of different sizes (Kumpula et al 2007), but, in this case, when the networks come from a series from the same network being continuously reduced, this can at most shift the peak of maximum D marginally (Huss & Holme 2007). We note that there are several other ways, apart from maximizing equation (2.1), of dividing networks into clusters.…”

Section: Network Modularitymentioning

confidence: 99%

Model validation of simple-graph representations of metabolism

Holme

2009

J. R. Soc. Interface.

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The large-scale properties of chemical reaction systems, such as metabolism, can be studied with graph-based methods. To do this, one needs to reduce the information, lists of chemical reactions, available in databases. Even for the simplest type of graph representation, this reduction can be done in several ways. We investigate different simple network representations by testing how well they encode information about one biologically important network structure-network modularity (the propensity for edges to be clustered into dense groups that are sparsely connected between each other). To achieve this goal, we design a model of reaction systems where network modularity can be controlled and measure how well the reduction to simple graphs captures the modular structure of the model reaction system. We find that the network types that best capture the modular structure of the reaction system are substrate-product networks (where substrates are linked to products of a reaction) and substance networks (with edges between all substances participating in a reaction). Furthermore, we argue that the proposed model for reaction systems with tunable clustering is a general framework for studies of how reaction systems are affected by modularity. To this end, we investigate statistical properties of the model and find, among other things, that it recreates correlations between degree and mass of the molecules.

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Section: Network Modularitymentioning

confidence: 99%

Model validation of simple-graph representations of metabolism

Holme

2009

J. R. Soc. Interface.

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“…This avoids the problems of modularity-based methods [17,18,19], which may not properly resolve communities if their size distribution is broad. The LA mechanism, which is mainly responsible for introducing new links, generates at least one triangle per added link.…”

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confidence: 99%

Emergence of Communities in Weighted Networks

Kumpula¹,

Onnela

Saramäki³

et al. 2007

Phys. Rev. Lett.

216

215

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Topology and weights are closely related in weighted complex networks and this is reflected in their modular structure. We present a simple network model where the weights are generated dynamically and they shape the developing topology. By tuning a model parameter governing the importance of weights, the resulting networks undergo a gradual structural transition from a module free topology to one with communities. The model also reproduces many features of large social networks, including the "weak links" property.PACS numbers: 89.75. Hc, 87.16.Ac,89.75.Fb, Network theory has undergone a remarkable development over the last decade and has contributed significantly to our understanding of complex systems, ranging from genetic transcriptions to the Internet and human societies [1,2]. Many complex networks are structured in terms of modules, or communities, which are groups of nodes characterized by having more internal than external connections between them. Such a mesoscopic network structure is expected to play a concrete functional role. Consequently, it is an important problem to understand how the communities emerge during the growth of the network. Apart from these issues of topological nature, it is important to realize that many complex networks are weighted, i.e., the interaction between two nodes is characterized not only by the existence of a link but a link with a varying weight assigned to it. There are a number of examples, like traffic, metabolic or correlation based networks, which provide ample evidence that the weights have to be included in their analysis. In many cases the weights affect significantly the properties or function of these networks, e.g., disease spreading [3], synchronisation dynamics of oscillators [4], and motif statistics [5]. It is natural to expect that weights have an influence on the formation of communities, which is the very issue of our study.Earlier, coupled weight-topology dynamics have been used successfully in transport networks modeling [6], which, however, does not lead to community structure. We show that there are mechanisms, by which weights play a crucial role in community formation. While we believe this to be quite a general paradigm for community formation, we have chosen to explore it within the realm of social systems where large datasets have enabled looking into both the coupling of network topology and interaction strengths and properties of communities [7,8,9]. Understanding how the underlying microscopic mechanisms translate into mesoscopic communities and macroscopic social systems is a key problem in its own right and one that is accessible within the scope of sta- tistical physics.Large scale social networks are known to satisfy the weak links hypothesis [10] with the implication that weak links keep the network connected whereas strong links are mostly associated with communities [24]. This weighttopology coupling results from the microscopic mechanisms that govern the evolution of social networks. Network sociology identifies (a) cyclic closure...

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“…The majority of these algorithms classify the nodes into disjoint communities, and in most cases a global quantity called modularity [56,55] is used to evaluate the quality of the partitioning. However, as pointed out in [29,49], the modularity optimisation introduces a resolution limit in the clustering, and communities containing a smaller number of edges than √ M (where M is the total number of edges) cannot be resolved. One of the big advantages of the clique percolation method (CPM) is that it identifies communities as k-clique percolation clusters, and therefore, the algorithm is local, and does not suffer from resolution problems of this type [64,21].…”

Section: Applications: Community Finding and Clusteringmentioning

confidence: 99%

k-Clique Percolation and Clustering

Palla

Ábel

Farkas

et al. 2008

Bolyai Society Mathematical Studies

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We summarise recent results connected to the concept of k-clique percolation. This approach can be considered as a generalisation of edge percolation with a great potential as a community finding method in real-world graphs. We present a detailed study of the critical point for the appearance of a giant kclique percolation cluster in the Erdős-Rényi-graph. The observed transition is continuous and at the transition point the scaling of the giant component with the number of vertices is highly non-trivial. The concept is extended to weighted and directed graphs as well. Finally, we demonstrate the effectiveness of k-clique percolation as a community finding method via a series of real-world applications.

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Limited resolution in complex network community detection with Potts model approach

Cited by 152 publications

References 22 publications

Model validation of simple-graph representations of metabolism

Model validation of simple-graph representations of metabolism

Emergence of Communities in Weighted Networks

k-Clique Percolation and Clustering

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