Hierarchical Characterization of Complex Networks

Costa, Luciano da Fontoura; Silva, Filipi Nascimento

doi:10.1007/s10955-006-9130-y

Cited by 63 publications

(29 citation statements)

References 36 publications

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“…Connectivity among neighbors of a node is quantified by the clustering coefficient cc , which reflects how many of all possible connections between neighbors actually exist (Watts and Strogatz, 1998; Kaiser et al, 2007a). The hierarchical clustering coefficient of level two cc 2 extends this concept to connections between neighbors’ neighbors (Costa and Silva, 2006). To what degree a node's neighbors connect to the same target is quantified by the locality index loc , which is based on the matching index (e.g., Kaiser and Hilgetag, 2004a).…”

Section: Methodsmentioning

confidence: 99%

Integrating Temporal and Spatial Scales: Human Structural Network Motifs Across Age and Region of Interest Size

Echtermeyer¹,

Han²,

Rotarska-Jagiela³

et al. 2011

Front. Neuroinform.

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Human brain networks can be characterized at different temporal or spatial scales given by the age of the subject or the spatial resolution of the neuroimaging method. Integration of data across scales can only be successful if the combined networks show a similar architecture. One way to compare networks is to look at spatial features, based on fiber length, and topological features of individual nodes where outlier nodes form single node motifs whose frequency yields a fingerprint of the network. Here, we observe how characteristic single node motifs change over age (12–23 years) and network size (414, 813, and 1615 nodes) for diffusion tensor imaging structural connectivity in healthy human subjects. First, we find the number and diversity of motifs in a network to be strongly correlated. Second, comparing different scales, the number and diversity of motifs varied across the temporal (subject age) and spatial (network resolution) scale: certain motifs might only occur at one spatial scale or for a certain age range. Third, regions of interest which show one motif at a lower resolution may show a range of motifs at a higher resolution which may or may not include the original motif at the lower resolution. Therefore, both the type and localization of motifs differ for different spatial resolutions. Our results also indicate that spatial resolution has a higher effect on topological measures whereas spatial measures, based on fiber lengths, remain more comparable between resolutions. Therefore, spatial resolution is crucial when comparing characteristic node fingerprints given by topological and spatial network features. As node motifs are based on topological and spatial properties of brain connectivity networks, these conclusions are also relevant to other studies using connectome analysis.

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Section: Methodsmentioning

confidence: 99%

Integrating Temporal and Spatial Scales: Human Structural Network Motifs Across Age and Region of Interest Size

Echtermeyer¹,

Han²,

Rotarska-Jagiela³

et al. 2011

Front. Neuroinform.

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“…This measurement, which is related to the heterogeneity of the vector p, provides a generalization of the classical concept of hierarchical (or concentric) degree [19], as explained in Fig. 1.…”

Section: The Effective Number Of Accessible Nodesmentioning

confidence: 99%

“…The current work addresses these problems through the concept of accessibility [18], which quantifies, for a given source node, the number of effectively accessible nodes at a given distance and with respect to a specific dynamics. In this sense, this measure complements the traditional hierarchical degree [19], providing valuable information about the network structure. Note that accessibility takes into account not only the number of nodes at a given distance, but also the transition probabilities between the source and these nodes.…”

Section: Introductionmentioning

confidence: 99%

Effective number of accessed nodes in complex networks

2012

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The measurement called accessibility has been proposed as a means to quantify the efficiency of the communication between nodes in complex networks. This article reports results regarding the properties of accessibility, including its relationship with the average minimal time to visit all nodes reachable after h steps along a random walk starting from a source, as well as the number of nodes that are visited after a finite period of time. We characterize the relationship between accessibility and the average number of walks required in order to visit all reachable nodes (the exploration time), conjecture that the maximum accessibility implies the minimal exploration time, and confirm the relationship between the accessibility values and the number of nodes visited after a basic time unit. The latter relationship is investigated with respect to three types of dynamics: traditional random walks, self-avoiding random walks, and preferential random walks.

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“…2, 3, ...) from that specific node. 6 In particular, the hierarchical degree of a node for hierarchical level i corresponds to the number of edges connecting the nodes at distance i to the nodes at distance i + 1. The hierarchical clustering coefficient of a given node for hierarchical level i is calculated in the same way as the traditional clustering measurement, but considering the edges between the nodes at distance i and the nodes at distance i + 1.…”

Section: Hierarchical Measurementsmentioning

confidence: 99%

Complex network representation of textures: new perspectives for texture characterization and classification

Chalumeau

Laligant

Costa³

et al. 2006

SPIE Proceedings

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Texture analysis represents one of the main areas in image processing and computer vision. The current article describes how complex networks have been used in order to represent and characterized textures. More specifically, networks are derived from the texture images by expressing pixels as network nodes and similarities between pixels as network edges. Then, measurements such as the node degree, strengths and clustering coefficient are used in order to quantify properties of the connectivity and topology of the analyzed networks. Because such properties are directly related to the structure of the respective texture images, they can be used as features for characterizing and classifying textures. The latter possibility is illustrated with respect to images of textures, DNA chaos game, and faces. The possibility of using the network representations as a subsidy for DNA characterization is also discussed in this work.

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Hierarchical Characterization of Complex Networks

Cited by 63 publications

References 36 publications

Integrating Temporal and Spatial Scales: Human Structural Network Motifs Across Age and Region of Interest Size

Integrating Temporal and Spatial Scales: Human Structural Network Motifs Across Age and Region of Interest Size

Effective number of accessed nodes in complex networks

Complex network representation of textures: new perspectives for texture characterization and classification

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