Key Node Ranking in Complex Networks: A Novel Entropy and Mutual Information-Based Approach

Abstract

Numerous problems in many fields can be solved effectively through the approach of modeling by complex network analysis. Finding key nodes is one of the most important and challenging problems in network analysis. In previous studies, methods have been proposed to identify key nodes. However, they rely mainly on a limited field of local information, lack large-scale access to global information, and are also usually NP-hard. In this paper, a novel entropy and mutual information-based centrality approach (EMI) is proposed, which attempts to capture a far wider range and a greater abundance of information for assessing how vital a node is. We have developed countermeasures to assess the influence of nodes: EMI is no longer confined to neighbor nodes, and both topological and digital network characteristics are taken into account. We employ mutual information to fix a flaw that exists in many methods. Experiments on real-world connected networks demonstrate the outstanding performance of the proposed approach in both correctness and efficiency as compared with previous approaches.

On the Entropy of Events under Eventually Global Inflated or Deflated Probability Constraints. Application to the Supervision of Epidemic Models under Vaccination Controls

“…2 j+1 = 1 then m 1 ≥ −1 so that H 0 ≥ 0 and H 1 ≥ H 0 ≥ 0. Furthermore, (26) and (27) imply that m 1 ∈ [−1, 0] and m 0 ∈ [0, 1]. The proof of Property (i) has been completed.…”

“…where µ = 2.0 years −1 is the growth and death rate of the population, ε = 1.0 years −1 , δ = 0.1 days −1 , γ = 0.02 days −1 are the instantaneous per capita rates of leaving the exposed, infected and recovered stages, respectively, and V(t) denotes the vaccination. This model fits in the structure given by (26) where u(t) = V(t) acts as the control command. The initial conditions are given by S(0) = E(0) = I(0) = R(0) = 0.1.…”

“…is the growth and death rate of the population, are the instantaneous per capita rates of leaving the exposed, infected and recovered stages, respectively, and) t ( Vdenotes the vaccination. This model fits in the structure given by(26) where…”

“…See, for instance, [14][15][16]25] and some of the references therein. In particular, entropy tools for analysis are mixed with differential-type models in [16,25,26]. Also, the control techniques are appropriate for studies of alternative biological problems, [27][28][29] and, in particular, for implementation of decentralized control techniques in patchy environments where several nodes are interlaced, [27,29].…”

Influential Nodes Identification in Complex Networks via Information Entropy

“…So he measured node importance by entropy variation [ 48 ] which calculates the change of graph entropy when that node is removed. In order to capture a wider range and greater abundance of information, Li et al put forward entropy and mutual information-based centrality approach (EMI) [ 49 ] to take both topological and digital network characteristics into account. Fei et al used relative entropy [ 50 ] to choose appropriate centrality measures when dealing with different networks.…”