Regular lattice with random weights assigned to the first and second closed neighbors. An agent leaves a given site and moves according to the rule of not returning to the last μ visited sites. The trajectory is composed of a transient time (orange sites) and an attractor (green sites).
Example of the first steps of an agent using memory of size μ = 1 and movement rule of going to the closest vertex.
Example of the first steps of an agent using memory of size μ = 1 and movement rule of going to the furthest vertex.
Histograms of walk length for different complex network models built using N = 50000 and vertices degree mean .
Histograms of walk length for number of vertices varying from N = 10000 to 50000 on the small-world model.
Histograms of walk length for degree mean varying from to 50 on the small-world model.
PCA projection for 4000 networks obtained by using Erdõs-Rényi, geographical network, small-world and scale-free. Networks were built with N = 1000 and , and the walks were performed with μ = 5. (a) The walker chooses to go to the closest site, and (b) the walker goes to the furthest one.
PCA projection for complex network models built with N = 1000 and using deterministic walks with different values of memory and din = [min, max]. (a) μ = 0, (b) μ = 1, (c) μ = 2, (d) μ = 3, (e) μ = 4 and (f) μ = 5.
PCA projection of signature vectors composed by the concatenation of memories 0, 1, 2, 3, 4, and 5. The signatures vectors were extracted from complex networks built with N = 1000 and .
Classification results for different percentages on the number of vertices.
Scatter plot matrix for the first three features obtained from 4000 complex networks.
Dendrogram of the class means using the manova takes a set of grouped data composed by the features extracted using the partially self-avoiding walks characteristics of 1000 complex networks for each class (random network, scale-free, geographical, and small-world).
Classification results using different values of α in the nonlinear Barabási-Albert model. When α = 1, the nonlinear Barabási-Albert and the Barabási-Albert model are the same.
Statistics of the histograms for different complex network models.
Statistics of the histograms for different values of N on the small-world model.
Statistics of the histograms for different values of on the small-world model.
Correct classification rate for with different values of μ and movement rule din.
Correct classification rate for composed by the concatenation of values μ.
Classification results of different scale-free models.
Comparison between measurements extracted from the complex networks.
Comparison between combination of measurements.
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