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In order to connect the concepts with these structural roles, each concept in the network has been ranked based on its total degree centrality (C D) and its betweenness centrality (C B).
The first five features are the following: degree normalized by the maximum degree in the network D, observed infected neighbor ratio R (the fraction of infected neighbors in observed neighbors), betweenness centrality C (b), closeness centrality C (c), and eigenvector centrality C (e) [3].
The relative density R C (i) of node i is the ratio of the minimum centrality C min to node i's density C i in a cluster.
So, although actor 4 has high betweeness as a node centrality, C EVB is reduced due to a lower scoring edge betweeness neighborhood.
Betweenness centrality (C B) is the sum of the proportions of the shortest paths a node lies on for every pair of nodes (out of all shortest paths for each pair).
In this simulation, the static attractiveness S of each street segment (i.e. each link in the network) is taken to be directly proportional to its betweenness centrality C b, in line with the reasoning outlined previously.
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Degree centrality is: C(D^{i} ) = mathop sum limits_{k ne i}^{n} A_{i,j} (1).
More technically, let σ ( i, j ) be the number of shortest paths between i and j (a shortest path does not have to be unique) and let σ l ( i, j ) be the number of shortest paths between i and j that pass l, then l's betweenness centrality is C B ( l ) = ∑ j ∑ i ≠ j σ l ( i, j ) σ ( i, j ).
Each link e i can also be assigned a priori two values: a fundamental basic attractiveness B i (summarising static features likely to have an influence on burglary, such as security and affluence) and a centrality measure C i (such as betweenness) determined by the network structure.
In our studies on the relation of correlation networks and metabolic reaction networks, we additionally used the centrality σ C [ 4, 35] to compare both types of networks.
Measures of cohesion (clustering coefficient; W CC = 0.98) and shortest-path centrality (W C = 0.14) were also informative for the highly inter-connected networks (Table 1).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com