Bridge and brick motifs in complex networks

Huang, Chung Yuan; Sun, Chuen Tsai; Cheng, Chia Ying; Hsieh, Ji Lung

doi:10.1016/j.physa.2006.11.014

Cited by 20 publications

(8 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Lancichinetti et al analyzed the statistical properties of communities in five categories of real complex networks, and found that communities detected in networks of the same category display similar structural characteristics [39]. Motifs, which are defined as subgraphs that occur much more often than expected in a random network, play a significant role in our understanding of the interplay between the structures and dynamics of real complex networks [40][41][42][43][44][45].…”

Section: Introductionmentioning

confidence: 99%

Emergence of Scale-Free Close-Knit Friendship Structure in Online Social Networks

et al. 2012

View full text Add to dashboard Cite

Although the structural properties of online social networks have attracted much attention, the properties of the close-knit friendship structures remain an important question. Here, we mainly focus on how these mesoscale structures are affected by the local and global structural properties. Analyzing the data of four large-scale online social networks reveals several common structural properties. It is found that not only the local structures given by the indegree, outdegree, and reciprocal degree distributions follow a similar scaling behavior, the mesoscale structures represented by the distributions of close-knit friendship structures also exhibit a similar scaling law. The degree correlation is very weak over a wide range of the degrees. We propose a simple directed network model that captures the observed properties. The model incorporates two mechanisms: reciprocation and preferential attachment. Through rate equation analysis of our model, the local-scale and mesoscale structural properties are derived. In the local-scale, the same scaling behavior of indegree and outdegree distributions stems from indegree and outdegree of nodes both growing as the same function of the introduction time, and the reciprocal degree distribution also shows the same power-law due to the linear relationship between the reciprocal degree and in/outdegree of nodes. In the mesoscale, the distributions of four closed triples representing close-knit friendship structures are found to exhibit identical power-laws, a behavior attributed to the negligible degree correlations. Intriguingly, all the power-law exponents of the distributions in the local-scale and mesoscale depend only on one global parameter, the mean in/outdegree, while both the mean in/outdegree and the reciprocity together determine the ratio of the reciprocal degree of a node to its in/outdegree. Structural properties of numerical simulated networks are analyzed and compared with each of the four real networks. This work helps understand the interplay between structures on different scales in online social networks.

show abstract

Section: Introductionmentioning

confidence: 99%

Emergence of Scale-Free Close-Knit Friendship Structure in Online Social Networks

et al. 2012

View full text Add to dashboard Cite

show abstract

“…While at the global scale we can summarize the overall architecture [2][3][4], at the local scale we can detect which nodes are the most relevant for the organization and functioning of a network [5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Communicability betweenness in complex networks

Estrada¹,

Higham²,

Hatano

2009

Physica A: Statistical Mechanics and its Applications

114

View full text Add to dashboard Cite

Betweenness measures provide quantitative tools to pick out fine details from the massive amount of interaction data that is available from large complex networks. They allow us to study the extent to which a node takes part when information is passed around the network. Nodes with high betweenness may be regarded as key players that have a highly active role. At one extreme, betweenness has been defined by considering information passing only through the shortest paths between pairs of nodes. At the other extreme, an alternative type of betweenness has been defined by considering all possible walks of any length. In this work, we propose a betweenness measure that lies between these two opposing viewpoints. We allow information to pass through all possible routes, but introduce a scaling so that longer walks carry less importance. This new definition shares a similar philosophy to that of communicability for pairs of nodes in a network, which was introduced by Estrada and Hatano (Phys. Rev. E 77 (2008) 036111). Having defined this new communicability betweenness measure, we show that it can be characterized neatly in terms of the exponential of the adjacency matrix. We also show that this measure is closely related to a Fréchet derivative of the matrix exponential. This allows us to conclude that it also describes network sensitivity when the edges of a given node are subject to infinitesimally small perturbations. Using illustrative synthetic and real life networks, we show that the new betweenness measure behaves differently to existing versions, and in particular we show that it recovers meaningful biological information from a protein-protein interaction network.3

show abstract

“…The number of species involved is usually large and the types of interactions diverse. Studies have shown that the structure of these networks is intimately connected with ecological and evolutionary processes, and understanding their general properties may tell us something about their origin and stability [9,[23][24][25]. In this work we have considered the relation between network structure and stability of species [26] under catastrophic events for a simple predator-prey network with four species.…”

Section: Discussionmentioning

confidence: 99%