Fig 1.
Description of the diffusion community detection workflow A: Decoupling of a spatial network into geometric and topological information. Credit for the base layer city map that illustrates the spatial network: Rue d’Aubagne, Marseille, France OpenStreetMap B: We consider a random walker on the topological network C: Nodes of the network are embedded into the diffusion space D: Diffusion communities are clusters made in the diffusion space E: These communities are interpreted as: random walkers departing from nodes of the same community follow correlated probability of presence fields F: Nodes are close in the diffusion space if they are highly connected through random walks. Dash lines represent random walks trajectories through nodes not represented on the sketch.
Table 1.
Summary of the characteristics the considered networks.
Fig 2.
A: Degree distribution B: Probability of presence departing from one chosen node in time C: 100 diffusion communities at relaxation time τ shown in the diffusion space in the dimensions 1 and 2 (respectively 2nd and 3rd columns of X(τ) = ΨΛτ, the first column for dimension 0 being filled with only value 1) D: The 100 diffusion communities shown in the physical space (right panel).
Fig 3.
The LNCN is spatially coherent.
A-E 100 diffusion communities for the HVor, HVor rewired 2%, HVor rewired 5%, HVor rewired 10%, HVor rewired 20%. Each color represent a community. In the HVor and PVor, there is respectively 95% and 99% of nodes that belong to a unique community among the 100 communities imposed by k-means algorithm F: The mean Cheeger index across all communities for each null model.
increases as the rewiring percentage increases departing from the HVor. Compared with this series of null models, LNCN mean Cheeger mixing value is higher than the HVor and lower than the HVor rewired 2%.
Fig 4.
The LNCN network displays a level of heterogeneity higher than the HCN and the Random network and lower than the PCN.
A,B,C,D: < pin >C (t) and < pout >C (t) box plots, respectively for the LNCN,HVor, PVor and Random network. The dash lines mark the relaxation times. E: The maximal standard deviation over all times of < pin >C (t) and < pout >C (t).
Fig 5.
A: < pin >C (t = 935) and < pout >C (t = 935) for each community at biological scan time B: On the left panel, < pin >C (t = 935) at biological scan time showed as percentage of the mean value across the 100 communities, shown for each of the 100 communities, ranked from smallest to largest value. The five communities with smallest values of < pin >C are shown as colored dots. The same plot for < pout >C is visually identical so we show only < pin >C. The same 5 communities have both lowest < pin >C and < pout >C. On the right panel these five communities locations are shown with the same colors. C,D: On the left panels, Cheeger mixing value of each community represented as percentage of the mean value across the 100 communities, shown for the 100 communities, ranked from smallest to largest value. The five communities with smallest (C), and highest highest (D) values are shown as colored dots. On the right panels, these communities locations are shown with the same colors.