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46
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such
Detecting the overlapping and hierarchical community structure in complex networks
 New J. Phys. p
, 2009
"... Abstract. Many networks in nature, society and technology are characterized by a mesoscopic level of organization, with groups of nodes forming tightly connected units, called communities or modules, that are only weakly linked to each other. Uncovering this community structure is one of the most im ..."
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Cited by 143 (0 self)
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Abstract. Many networks in nature, society and technology are characterized by a mesoscopic level of organization, with groups of nodes forming tightly connected units, called communities or modules, that are only weakly linked to each other. Uncovering this community structure is one of the most important problems in the field of complex networks. Networks often show a hierarchical organization, with communities embedded within other communities; moreover, nodes can be shared between different communities. Here we present the first algorithm that finds both overlapping communities and the hierarchical structure. The method is based on the local optimization of a fitness function. Community structure is revealed by peaks in the fitness histogram. The resolution can be tuned by a parameter enabling to investigate different hierarchical levels of organization. Tests on real and artificial networks give excellent results. PACS numbers: 89.75.k, 89.75.Hc, 05.40a, 89.75.Fb, 87.23.GeDetecting the overlapping and hierarchical community structure in complex networks 2 1.
Statistical significance of communities in networks
 Physical Review E
"... Community structure is one of the main structural features of networks, revealing both their internal organization and the similarity of their elementary units. Despite the large variety of methods proposed to detect communities in graphs, there is a big need for multipurpose techniques, able to ha ..."
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Cited by 58 (2 self)
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Community structure is one of the main structural features of networks, revealing both their internal organization and the similarity of their elementary units. Despite the large variety of methods proposed to detect communities in graphs, there is a big need for multipurpose techniques, able to handle different types of datasets and the subtleties of community structure. In this paper we present OSLOM (Order Statistics Local Optimization Method), the first method capable to detect clusters in networks accounting for edge directions, edge weights, overlapping communities, hierarchies and community dynamics. It is based on the local optimization of a fitness function expressing the statistical significance of clusters with respect to random fluctuations, which is estimated with tools of Extreme and Order Statistics. OSLOM can be used alone or as a refinement procedure of partitions/covers delivered by other techniques. We have also implemented sequential algorithms combining OSLOM with other fast techniques, so that the community structure of very large networks can be uncovered. Our method has a comparable performance as the best existing algorithms on artificial benchmark graphs. Several applications on real networks are shown as well. OSLOM is implemented in a freely available software
Uncovering individual and collective human dynamics from mobile phone records
 Journal of Physics A: Mathematical and Theoretical
"... from mobile phone records ..."
Community Structure in Graphs
, 2007
"... Graph vertices are often organized into groups that seem to live fairly independently of the rest of the graph, with which they share but a few edges, whereas the relationships between group members are stronger, as shown by the large number of mutual connections. Such groups of vertices, or communi ..."
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Cited by 44 (0 self)
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Graph vertices are often organized into groups that seem to live fairly independently of the rest of the graph, with which they share but a few edges, whereas the relationships between group members are stronger, as shown by the large number of mutual connections. Such groups of vertices, or communities, can be considered as independent compartments of a graph. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. The task is very hard, though, both conceptually, due to the ambiguity in the definition of community and in the discrimination of different partitions and practically, because algorithms must find “good ” partitions among an exponentially large number of them. Other complications are represented by the possible occurrence of hierarchies, i.e. communities which are nested inside larger communities, and by the existence of overlaps between communities, due to the presence of nodes belonging to more groups. All these aspects are dealt with in some detail and many methods are described, from traditional approaches used in computer science and sociology to recent techniques developed mostly within statistical physics.
Directed network modules
 New Journal of Physics
"... Abstract. The inclusion of link weights into the analysis of network properties allows a deeper insight into the (often overlapping) modular structure of realworld webs. We introduce a clustering algorithm (CPMw, Clique Percolation Method with weights) for weighted networks based on the concept of ..."
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Cited by 31 (0 self)
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Abstract. The inclusion of link weights into the analysis of network properties allows a deeper insight into the (often overlapping) modular structure of realworld webs. We introduce a clustering algorithm (CPMw, Clique Percolation Method with weights) for weighted networks based on the concept of percolating kcliques with high enough intensity. The algorithm allows overlaps between the modules. First, we give detailed analytical and numerical results about the critical point of weighted kclique percolation on (weighted) ErdősRényi graphs. Then, for a scientist collaboration web and a stock correlation graph we compute threelink weight correlations and with the CPMw the weighted modules. After reshuffling link weights in both networks and computing the same quantities for the randomised control graphs as well, we show that groups of 3 or more strong links prefer to cluster together in both original graphs. PACS numbers: 02.70.Rr, 05.10.a, 89.20.a, 89.75.k 89.75.HcWeighted network modules 2 1.
The structure of interurban traffic: a weighted network analysis. Environment and Planning B doi:10.1068/b32128
, 2007
"... We study the structure of the network representing the interurban commuting traffic of the Sardinia region, Italy, which amounts to 375 municipalities and 1,600,000 inhabitants. We use a weighted network representation where vertices correspond to towns and the edges to the actual commuting flows am ..."
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Cited by 18 (1 self)
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We study the structure of the network representing the interurban commuting traffic of the Sardinia region, Italy, which amounts to 375 municipalities and 1,600,000 inhabitants. We use a weighted network representation where vertices correspond to towns and the edges to the actual commuting flows among those. We characterize quantitatively both the topological and weighted properties of the resulting network. Interestingly, the statistical properties of commuting traffic exhibit complex features and nontrivial relations with the underlying topology. We characterize quantitatively the traffic backbone among large cities and we give evidences for a very high heterogeneity of the commuter flows around large cities. We also discuss the interplay between the topological and dynamical properties of the network as well as their relation with sociodemographic variables such as population and monthly income. This analysis may be useful at various stages in environmental planning and provides analytical tools for a wide spectrum of applications ranging from impact evaluation to decisionmaking and planning support. PACS numbers: 89.75.k,87.23.Ge, 05.40.a I.
Consensus formation on coevolving networks: groups ’ formation and structure
, 801
"... We study the effect of adaptivity on a social model of opinion dynamics and consensus formation. We analyze how the adaptivity of the network of contacts between agents to the underlying social dynamics affects the size and topological properties of groups and the convergence time to the stable fina ..."
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Cited by 7 (0 self)
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We study the effect of adaptivity on a social model of opinion dynamics and consensus formation. We analyze how the adaptivity of the network of contacts between agents to the underlying social dynamics affects the size and topological properties of groups and the convergence time to the stable final state. We find that, while on static networks these properties are determined by percolation phenomena, on adaptive networks the rewiring process leads to different behaviors: Adaptive rewiring fosters group formation by enhancing communication between agents of similar opinion, though it also makes possible the division of clusters. We show how the convergence time is determined by the characteristic time of link rearrangement. We finally investigate how the adaptivity yields nontrivial correlations between the internal topology and the size of the groups of agreeing agents.
Structure and growth of weighted networks
 New Journal of Physics
, 2010
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A (2012) Reliability of optimal linear projection of growing scalefree network. Int J of Bifurcat Chaos
"... Singular Value Decomposition (SVD) is a technique based on linear projection theory, which has been frequently used for data analysis. It constitutes an optimal (in the sense of least squares) decomposition of a matrix in the most relevant directions of the data variance. Usually, this information i ..."
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Cited by 2 (2 self)
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Singular Value Decomposition (SVD) is a technique based on linear projection theory, which has been frequently used for data analysis. It constitutes an optimal (in the sense of least squares) decomposition of a matrix in the most relevant directions of the data variance. Usually, this information is used to reduce the dimensionality of the data set in a few principal projection directions, this is called Truncated Singular Value Decomposition (TSVD). In situations where the data is continuously changing, the projection might become obsolete. Since the change rate of data can be fast, it is an interesting question whether the TSVD projection of the initial data is reliable. In the case of complex networks, this scenario is particularly important when considering network growth. Here we study the reliability of the TSVD projection of growing scalefree networks, monitoring its evolution at global and local scales.