Clustering in complex directed networks

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 76, Issue 2, 2007, Pages

  Fagiolo, Giorgio ^a  

^a SCUOLA SUPERIORE SANT ANNA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; DATA FLOW ANALYSIS; GRAPH THEORY;

CLUSTERING COEFFICIENT (CC); RANDOM GRAPHS; UNDIRECTED GRAPHS;

LARGE SCALE SYSTEMS;

EID: 34548065453     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.76.026107     Document Type: Article

References (44)

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33. Of course, by a symmetry argument, they actually reduce to four different distinct patterns (e.g., those in the first column). We will keep the classification in eight types for the sake of exposition.
34. The CC in Eq. 10 is similar to that presented by but takes explicitly into account edge directionality in computing the maximum number of directed triangles (TiD). Conversely, set TiD = di (di -1).
35. That is, wij is a random variable equal to zero with probability 1-p and equal to a U (0,1] with probability p. Of course this admittedly naïve assumption is made for mathematical convenience to benchmark our results in a setup where one is completely ignorant about the true (observed) weight distribution. In empirical applications, one would hardly expect observed weights to follow such a trivial distribution and more realistic assumptions should be made. For example, the expected value of CCs might be computed by bootstrapping (i.e., reshuffling) the observed empirical distribution of weights in W across the same topological graph structure, as defined by the observed adjacency matrix A. See also below.
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