Core-like groups result in invalidation of identifying super-spreader by k-shell decomposition (1409.5187v2)

Abstract: Identifying the most influential spreaders is an important issue in understanding and controlling spreading processes on complex networks. Recent studies showed that nodes located in the core of a network as identified by the k-shell decomposition are the most influential spreaders. However, through a great deal of numerical simulations, we observe that not in all real networks do nodes in high shells are very influential: in some networks the core nodes are the most influential which we call true core, while in others nodes in high shells, even the innermost core, are not good spreaders which we call core-like group. By analyzing the k-core structure of the networks, we find that the true core of a network links diversely to the shells of the network, while the core-like group links very locally within the group. For nodes in the core-like group, the k-shell index cannot reflect their location importance in the network. We further introduce a measure based on the link diversity of shells to effectively distinguish the true core and core-like group, and identify core-like groups throughout the networks. Our findings help to better understand the structural features of real networks and influential nodes.

• The paper demonstrates that k-shell decomposition can fail to identify true super-spreaders due to the existence of 'core-like groups' with localized connectivity.
• Numerical simulations on real networks using the SIR model show core nodes in some networks ('core-like groups') have significantly lower spreading efficacy than expected.
• The study proposes incorporating internal structural features like link diversity alongside k-shell to improve accurate identification of influential nodes for applications like epidemic control.

Analysis of Core-Like Groups in Network Spreading Processes via k-Shell Decomposition

In the paper conducted by Liu et al., the authors address the problem of identifying super-spreader nodes in complex networks through k-shell decomposition. This work critically examines the intra-network structural features that determine the efficacy of nodes as spreaders of information or diseases, emphasizing the limitations of relying solely on a node's k-shell index as a predictor of spreading influence.

Key Findings and Methodology

The paper's central contention is that nodes positioned in the core of a network, as determined by k-shell decomposition, are not universally the most influential spreaders. Notably, the authors define two types of network cores: "true cores," which have a high capability for information spread due to their diverse linkage to multiple network layers, and "core-like groups," which, despite their k-shell indices, are less influential because of their local and densely-packed connectivity.

The research supports this claim through extensive numerical simulations and empirical analysis of nine real-world networks, varying from Internet router ecosystems to social media interactions. The authors quantify node influence based on the spread size in a Susceptible-Infected-Recovered (SIR) model, analyzing imprecision functions for both coreness and degree centrality measures. They demonstrate that in some networks, like Router, Emailcontact, and AS, core nodes correspond to high spreading efficiency, aligning with the "true cores" concept. However, in networks such as the Email, CA-Hep, and Hamster, core nodes exhibit lower spreading efficacy, characterizing the core-like groups.

Implications and Analytical Advances

The foundational insight of this paper is the revelation that k-shell decomposition, while computationally efficient, cannot fully account for the varying connectivity patterns within high-shell nodes. This paper introduces a concrete method of combining link diversity analysis with k-shell indices, which significantly improves the identification of influential nodes by highlighting core-like groups. The analysis employs entropy measures to evaluate the linkage diversity from core nodes to other layers, offering a quantitative framework to distinguish true cores from core-like groups.

These findings imply the necessity of revisiting structural analysis tools employed within network science for tasks like epidemic prevention strategies or information optimization. The distinction between core structures elucidated in this paper encourages a nuanced approach to employing centrality measures within different network types. In practice, considering link diversity alongside traditional decomposition can refine strategies for targeted interventions in social, technological, and biological networks.

Speculations for Future Directions

The work by Liu et al. establishes the groundwork for more sophisticated models of network analysis that incorporate structural heterogeneity at deeper levels than previously considered. Future research could further explore the temporal dynamics of core-like groups' influence over time within evolving networks or apply these findings to multiplex and weighted network structures where node influence may be multifactorial and context-dependent. Furthermore, expanding upon entropy-based methodologies could refine robustness analyses of network resilience, especially in weighted or dynamically evolving systems.

In conclusion, this research contributes a significant advancement to the understanding of influential spreader identification by critiquing and extending the k-shell decomposition methodology. By recognizing the conditions under which k-shell indices become insufficient, the paper encourages a more comprehensive integration of network topology features into the spread dynamics discourse.