Fig 1.
Local clustering coefficient of node 1.
Possible local clustering coefficient at node 1 (orange node or C1) with degrees k1 = 4 on an undirected graph. The blue dashed lines represent the possible connections between the neighbors, and the red solid lines represent the triangles between the neighbors of node 1.
Fig 2.
Losses faced by a computer (node).
Two types of losses are faced by node v in a network during the time interval [t0, T]. L is losses caused by data damage, and R is losses caused by system downtime.
Fig 3.
Dynamics of the modified Markov-based model.
The dynamics of the infection and recovery processes of a network follow a modified ε-SIS model with local coefficient clustering factors f(Cv) for time steps t1, t2, and t3. Red nodes indicate that the nodes are infected, and blue nodes indicate that the nodes are vulnerable at a certain time.
Fig 4.
Study case in 4-regular graph.
Realization of a random 4-regular graph with the order n = 20.
Fig 5.
Average local clustering coefficient.
Relationship between the average clustering coefficient and the order of graph n = 10, 12, 14, ⋯, 100 for several different k = 1, 2, ⋯, 9.
Fig 6.
Representation of the inhibition of the epidemic by the clustering coefficient.
The inhibition considers three functions, namely, linear (f(Cv) = −Cv + 1), quadratic (), and exponential (
) functions.
Fig 7.
The upper bounds for infection probabilities.
A comparison between upper bounds for infection probabilities without and with clustering coefficients using three types of inhibition functions (linear, quadratic, and exponential). The red box reflects the upper bound for resizing all figures at t = [3,20], and the extension outcomes can be seen inside each figure.
Table 1.
Characteristics of clustering coefficients for nodes in a 4-regular graph topology (Fig 4).
Fig 8.
TN and UB relationship of twenty nodes in a 4-regular graph on linear, quadratic, and exponential functions.
Fig 9.
Convergence of the Monte Carlo simulation.
Convergence for Infection Mean, Loss Mean, and Premiums.
Fig 10.
Correlation between the total function of the clustering coefficient (TN) and the premium (P).
TN and P relationship of twenty nodes in a 4-regular graph on linear, quadratic, and exponential functions.
Table 2.
Premiums in a 4-regular graph topology (Fig 4).
Fig 11.
An email-Enron network with nodes representing email accounts or devices and links representing email exchange.
Table 3.
Characteristics of an email-Enron network.
Table 4.
Ten nodes were chosen from a total of 143 nodes.
They were selected based on their degree and uniqueness of behavior.
Table 5.
The premium of the ten selected nodes.
Premiums and confidence intervals (CI 95%) for selected nodes without clustering functions, and with clustering functions (quadratic, linear, exponential).
Fig 12.
Premium comparison for ten selected nodes.
Confidence interval plot with 95% CI without and with clustering coefficients.
Fig 13.
Boxplot of premium comparison of control variables (without CC).
Boxplot considers without CC and with CC (quadratic, linear, exponential).
Fig 14.
Bar plot and confidence interval plot of premiums for the whole network.
Comparison of the total premium (one network premium) in the absence and presence of CC. The text in the bar plot represents the percentage of premium modifications made to the premium without clustering coefficients for each quadratic, linear, and exponential inhibition function.
Fig 15.
Correlation between degrees (Deg), the total local clustering coefficient (Total C), the premium without CC (P), the premium with a quadratic function (P. QUA), the premium with a linear function (P. LIN), and the premium with an exponential function (P.EXP).