Benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities

Many complex networks display a mesoscopic structure with groups of nodes sharing many links with the other nodes in their group and comparatively few with nodes of different groups. This feature is known as community structure and encodes precious information about the organization and the function of the nodes. Many algorithms have been proposed but it is not yet clear how they should be tested. Recently we have proposed a general class of undirected and unweighted benchmark graphs, with heterogenous distributions of node degree and community size. An increasing attention has been recently devoted to develop algorithms able to consider the direction and the weight of the links, which require suitable benchmark graphs for testing. In this paper we extend the basic ideas behind our previous benchmark to generate directed and weighted networks with built-in community structure. We also consider the possibility that nodes belong to more communities, a feature occurring in real systems, like, e. g., social networks. As a practical application, we show how modularity optimization performs on our new benchmark.Comment: 9 pages, 13 figures. Final version published in Physical Review E. The code to create the benchmark graphs can be freely downloaded from http://santo.fortunato.googlepages.com/inthepress

Seeding for pervasively overlapping communities

In some social and biological networks, the majority of nodes belong to multiple communities. It has recently been shown that a number of the algorithms that are designed to detect overlapping communities do not perform well in such highly overlapping settings. Here, we consider one class of these algorithms, those which optimize a local fitness measure, typically by using a greedy heuristic to expand a seed into a community. We perform synthetic benchmarks which indicate that an appropriate seeding strategy becomes increasingly important as the extent of community overlap increases. We find that distinct cliques provide the best seeds. We find further support for this seeding strategy with benchmarks on a Facebook network and the yeast interactome.Comment: 8 Page

Changes in aromatic characteristics of loureiro and alvarinho wines during maturation

Changes in volatiles during maturation in bottles of monovarietal Vinhos Verdes wines from Loureiro and Alvarinho grape varieties, were followed by chemical and sensory analyses. Young wines and wines matured for 8 and 20 months were studied. The volatiles were determined by gas chromatography– mass spectrometry (GC-MS) after extraction on XAD-2 resin. Straight chain fatty acid ethyl esters and acetates of fusel alcohols decreased quicker for Loureiro wine, while the increase in ethyl esters of branched fatty acids was similar for both varieties. Linalool, Ho-trienol, a-terpineol and b-damascenone could be used to differentiate between each variety. However, linalool decreased to negligible values after 20 months of maturation. b-Damascenone decreased but remained high enough to be useful for differentiating each variety. Sensory analysis indicated a decrease of tropical fruit and tree fruit characters with conservation time for Alvarinho wine, and the opposite for Loureiro; moreover, citrus fruit character decreased in both varietiesCentre of Biological Engineering of Universidade do Minho (CEB-UM); Estação Vitivinícola Amândio Galhano (EVAG); Solar de Serrade; Comissão de Viticultura da Região dos Vinhos Verdes

Soil and climatic influence on the free and glycosidically bound volatiles of grapes from two white varieties from vinhos verdes region

The Vinhos Verdes Region is situated in the northwest of Portugal. The Atlantic Ocean and the relief markedly influence the climate. This region is in Viticultural Zone C I a) of the Winegrowing Regions of the European Communities. The produced wine is unique and its specific characteristics are mainly due to the climate and soil. The white Vinho Verde is softly alcoholic, with a delicate, fresh and fruity bouquet. In this work we investigated the influence of the climate and the soil on the volatile compounds of grapes from two autochthonous white grape varieties, Alvarinho and Loureiro, in two sub-regions for each one of them (Alvarinho - Monção and Lima; Loureiro - Lima and Cávado). The research was carried out during three years: 1996, 1997 and 1998. We found out that the global characteristics of the grapes from the two varieties depend on the harvest factor (climate) rather than on the sub-region where the vine is planted. The characteristics of the soil have an even lesser influence on the variableness of the samples, although the Alvarinho variety picked in the Lima sub-region seems to have different characteristics

Différentiation des cépages portugais Loureiro et Alvarinho basée sur la composition monoterpénique libre

IBQF; Com. Vit. Região Vinhos Verdes (EVAG); Adega C.R. Monção; Casa da Tapada

Teneur en norisoprénoïdes en c13 des cépages Portugais loureiro et alvarinho

Les cépages portugais Loureiro et Alvarinho sont importants pour l'économie de la Région portugaise des "Vinhos Verdes". Ces deux variétés de raisin sont à l'origine de vins blancs monovarietaux réputés, présentant des caractéristiques aromatiques intéressantes. Ce travail a pour objectif d'approfondir les connaissances sur l'une des composantes du potentiel aromatique de ces deux cépages, les norisoprénoïdes en C13, composés dérivés des caroténoïdes. Les essais ont été conduits sur des échantillons de raisins du millésime 1996, deux de Loureiro et deux d'Alvarinho, provenant de deux sub-régions des "Vinhos Verdes", les plus recommandées pour l'obtention de vin de qualité; un troisième échantillon d'Alvarinho provient d'un type de sol différent. Quatorze composés norisoprénoïdes en C13 ont été identifiés et quantifiés dans la fraction glycosylée des deux variétés. Une analyse en composantes principales utilisant les teneurs en ces composés permet de distinguer nettement les deux cépages. L'Alvarinho est un peu plus riche que le Loureiro, notamment en ce qui concerne le 3-oxo-7,8-dihydro-α-ionol, le 3-hydroxy-7,8-déhydro-β-ionol, le 3-oxo-α-ionol et la 3-hydroxy-β-damascone. Par contre le Loureiro contient des teneurs plus élevées en 3- hydroxy-7,8-dihydro-β-ionol.IBQF ; Ambassade de France au Portuga l; JNICT ; Comissão de Viticultura da Região dos Vinhos Verdes (EVAG) ; Adega C.R. Monção ; Casa da Tapada ; Solar de Serrade

Identifying Overlapping and Hierarchical Thematic Structures in Networks of Scholarly Papers: A Comparison of Three Approaches

We implemented three recently proposed approaches to the identification of overlapping and hierarchical substructures in graphs and applied the corresponding algorithms to a network of 492 information-science papers coupled via their cited sources. The thematic substructures obtained and overlaps produced by the three hierarchical cluster algorithms were compared to a content-based categorisation, which we based on the interpretation of titles and keywords. We defined sets of papers dealing with three topics located on different levels of aggregation: h-index, webometrics, and bibliometrics. We identified these topics with branches in the dendrograms produced by the three cluster algorithms and compared the overlapping topics they detected with one another and with the three pre-defined paper sets. We discuss the advantages and drawbacks of applying the three approaches to paper networks in research fields.Comment: 18 pages, 9 figure

Finding community structure in networks using the eigenvectors of matrices

We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as "modularity" over possible divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in networks and a new centrality measure that identifies those vertices that occupy central positions within the communities to which they belong. The algorithms and measures proposed are illustrated with applications to a variety of real-world complex networks.Comment: 22 pages, 8 figures, minor corrections in this versio

Detecting the overlapping and hierarchical community structure of complex networks

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.Comment: 20 pages, 8 figures. Final version published on New Journal of Physic