Fig. 2
From: The topology of the directed clique complex as a network invariant
Plots of the degree-filtered Euler characteristic for different networks. All networks were generated with \(n=40\) nodes chosen with a fixed ordering. a Barabasi–Albert Scale Free (SF) network (\(m = 10\)). b Erdős–Rényi Random Network (RN) (\(p = 0.2\)). c Newman–Watts–Strogatz Small World (SW) network (\(k = 20\), \(p = 0.4\)). The plots show the averaged curves (in-degrees as red dotted lines and out-degrees as blue solid lines) for \(N=50\) experiments for each type of network. Confidence bands correspond to 95 % intervals. The x-axis is normalized, expressing each filtration level as the degree of the vertices at that level divided by the maximum degree of vertices present in the network. This representation makes it possible to compare the plots for different networks. Notice that the variation range, the monotonicity and the comparison between the in- and the out-degree filtrations can be used to distinguish the different types of networks