Intensity and coherence of motifs in weighted complex networks.

By Jukka-Pekka Onnela, J. Saramaki, János Kertész, Kimmo K. Kaski. Physical review. E, Statistical, nonlinear, and soft matter physics, 2004

1,049 citations recorded by the source corpus.

The local structure of unweighted networks can be characterized by the number of times a subgraph appears in the network. The clustering coefficient, reflecting the local configuration of triangles, can be seen as a special case of this approach. In this paper we generalize this method for weighted networks. We introduce subgraph "intensity" as the geometric mean of its link weights "coherence" as the ratio of the geometric to the corresponding arithmetic mean. Using these measures, motif scores and clustering coefficient can be generalized to weighted networks. To demonstrate these concepts, we apply them to financial and metabolic networks and find that inclusion of weights may considerably modify the conclusions obtained from the study of unweighted characteristics.

Subfields: Computational Theory and Mathematics, Molecular Biology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8a882d9027e72ac8fd63cbf7e5be2dd4cfcd439f

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Citations in the corpus

Studying the human brain anatomical network via diffusion-weighted MRI and Graph Theory (2008, positive): “In a weighted graph, the clustering around a node i can be calculated as the geometric average of subgraph node weights (Onnela et al., 2005):”
Graph theoretical analysis of complex networks in the brain (2007, background): “It is also possible to define a weighted clustering coefficient, that takes into account both the weights between the reference vertex and its neighbours, as well as the weights of the edges between the neighbours [47].”
The evolution of the world trade web: a weighted-network analysis (2010, background): “This property can be measured by the clustering coeﬃcient (Watts and Strogatz, 1998; Szab´o et al., 2005), that is the percentage of pairs of i ’s nearest neighbors that are themselves partners.”
State of the aRt personality research: A tutorial on network analysis of personality data in R (2015, neutral): “Recently three formulations of clustering, the unweighted clustering coefficient (Watts & Strogatz, 1998), the index proposed by Onnela (2005) and the one proposed by Zhang and Horvath (2005) have been generalized to signed networks and the properties of such indices have been discussed in the…”
Clustering in weighted networks (2009, background): “Recently, there have been a number of attempts to extend the local clustering coefficient to the case of weighted networks (Barrat et al., 2004; Lopez-Fernandez, Robles and Gonzalez-Barahona, 2004; Onnela et al., 2005; Zhang and Horvath, 2005).”
GRETNA: a graph theoretical network analysis toolbox for imaging connectomics (2015, background): “clustering coefficient and characteristic path length (Watts and Strogatz, 1998; Onnela et al., 2005), local efficiency and global efficiency (Latora and Marchiori, 2001, 2003), modularity (Newman, 2006), assortativity (Newman, 2002; Leung and Chau, 2007), synchronization (Barahona and Pecora, 2002;”
The application of graph theoretical analysis to complex networks in the brain. (2007, neutral): “At this time, only few measures are available for the analysis of weighted graphs (Latora and Marchiori, 2001; Crucitti et al., 2003; Newman, 2004; Park et al., 2004; Barrat et al., 2004; Barthelemy et al., 2005; Onnela et al., 2005).”
Dynamic functional reorganization of the motor execution network after stroke. (2010, background): “Apart from the weighted clustering coefficient, we note that alternative definitions have recently been proposed (Onnela et al., 2005; Stam et al., 2009).”
Small-World Brain Networks Revisited (2016, background): “First, the weighted clustering coeﬃcient of node i can be deﬁned as where k i is the number of edges connected to node i , or degree of node i [87] (but see also [88, 89] for other similar deﬁnitions).”
Graph theoretical analysis of magnetoencephalographic functional connectivity in Alzheimer's disease. (2009, neutral): “Here we propose a simple definition, closely related to the proposal of Onnela et al. (2005), which only requires symmetry (wij = wji) and that 04wij4 1 holds.”
Weight-conserving characterization of complex functional brain networks (2011, background): “This view is related to notions of cluster stability (Bellec et al., 2010), connection-based modules (Ahn et al., 2010) and overlapping modules (Palla et al., 2005).”