Fig 1.
Illustrating the behavior of the descending order ranking scheme and the community-aware ranking scheme.
The nodes chosen are the top 3 nodes based on the Degree centrality (colored in red) and the Betweenness centrality (colored in blue).
Table 1.
Synthetic networks’ parameters generated by the LFR model.
Fig 2.
Impact of the community structure strength (μ) in synthetic networks.
The figures represent the relative difference of the outbreak size (ΔR) as a function of the fraction of initially infected nodes. The red curve indicates the relative performance difference of the community-aware ranking strategy with the descending order ranking for the six centrality measures under test. The mixing parameter (μ) varies while the other parameters, including the community size distribution exponent (θ = 2.7) and the degree distribution exponent (γ = 2.7), are fixed.
Fig 3.
The relative difference of the outbreak size (ΔR) as a function of the mixing parameter (μ) when fraction of initially infected nodes (fo) equals 0.15.
The color of the curve represents the centrality measures under study. (A) Synthetic networks with degree distribution γ = 2.7 and community size distribution θ = 2. (B) Synthetic networks with degree distribution γ = 2.7 and community size distribution θ = 2.7. (C) Synthetic networks with degree distribution γ = 2.7 and community size distribution θ = 3.
Fig 4.
Impact of the community size distribution exponent (θ) in synthetic networks.
The figures represent the relative difference of the outbreak size (ΔR) as a function of the fraction of initially infected nodes. The red curve indicates the relative performance difference of the community-aware ranks of the Degree and Katz centrality measures compared to the descending order ranks. The community size distribution exponent (θ) varies while the other parameters, including the mixing parameter (μ = 0.05) and the degree distribution exponent (γ = 2.7), are fixed.
Fig 5.
Impact of the degree distribution exponent (γ) in synthetic networks.
The figures represent the relative difference of the outbreak size (ΔR) as a function of the fraction of initially infected nodes. The red curve indicates the relative performance difference of the community-aware ranks of the Degree and Katz centrality measures compared to the descending order ranks. The degree distribution exponent (γ) varies while the other parameters, including the mixing parameter (μ = 0.05) and the community size distribution exponent (θ = 2.7), are fixed.
Fig 6.
The relative difference of the outbreak size (ΔR) as a function of the mixing parameter (μ) when fraction of initially infected nodes (fo) equals 0.15.
The color of the curve represents the centrality measures under study. (A) Synthetic networks with degree distribution γ = 2 and community size distribution θ = 2.7. (B) Synthetic networks with degree distribution γ = 2.7 and community size distribution θ = 2.7. (C) Synthetic networks with degree distribution γ = 3 and community size distribution θ = 2.7.
Fig 7.
Impact of the community structure strength (μ) in real-world networks.
The figures represent the relative difference of the outbreak size (ΔR) as a function of the fraction of initially infected nodes. The red curve indicates the relative performance difference of the community-aware ranking strategy with the descending order ranking for the six centrality measures under test. A strong, medium, and weak mixing parameter (μ) is derived based on the communities in real-world networks (U.S. Airports, Facebook Organizations, and Adolescent Health) identified by the Infomap community detection algorithm.
Fig 8.
Trends in the performance of the community-aware ranking scheme in real-world networks.
The figures represent the relative difference of the outbreak size (ΔR) as a function of the fraction of initially infected nodes. The red curve indicates the relative performance difference of the community-aware ranks of the Degree centrality compared to the descending order ranks. Communities are identified using Infomap. (A) Networks with a strong community structure strength. (B) Networks with a medium community structure strength. (C) Networks with a weak community structure strength.
Fig 9.
Top nodes selected based on the Degree and Closeness centrality measures according to the descending order and community-aware ranking schemes.
Communities of the Yeast Collins (A), EU Airlines (B), and AstroPh (C) networks are identified by Infomap. The top selected nodes (depicted in bigger sizes) amount to 15% of the network’s size.
Fig 10.
Impact of the community detection algorithm in real-world networks with strong, medium, and weak community structure strengths.
The figures represent the relative difference of the outbreak size (ΔR) as a function of the fraction of initially infected nodes. The red curve indicates the relative performance difference of the community-aware ranks of the Degree and Closeness centrality measures compared to the descending order ranks. (A) Communities identified using Infomap. (B) Communities identified using Louvain.
Fig 11.
Histograms of the community size distribution.
Communities are identified in Facebook Friends, Human Protein, and Bible Nouns by the Infomap (A) and Louvain (B) community detection algorithms.