Source-linked AI summary
Absence of influential spreaders in rumor dynamics
Javier Borge-Holthoefer, Yamir Moreno
TL;DR
The paper asks whether k-core position identifies influential spreaders in rumor dynamics as it does in epidemic models. It simulates rumor spreading on real-world communication networks and finds that spreading capacity is largely independent of coreness, while central nodes act as rumor firewalls. Thus, k-core index predicts distinct rumor-dynamics roles, but not privileged spreading capacity.
Problem
The paper examines whether coreness identifies influential spreaders in rumor dynamics, a setting relevant to information dissemination and social contagion.
Method
The authors simulate a three-state rumor model extensively on several real-world communication networks.
Results
Spreading capacity is nearly independent of a seed’s k-core index, while nodes in high cores become stiflers early and can interrupt rumor propagation.
Takeaways & Limitations
In rumor dynamics, k-core index identifies firewall-like roles rather than privileged spreaders, while high-core nodes gain earlier awareness of circulating information.
Abstract
from arXiv · showhide
Recent research [1] has suggested that coreness, and not degree, constitutes a better topological descriptor to identifying influential spreaders in complex networks. This hypothesis has been verified in the context of disease spreading. Here, we instead focus on rumor spreading models, which are more suited for social contagion and information propagation. To this end, we perform extensive computer simulations on top of several real-world networks and find opposite results. Namely, we show that the spreading capabilities of the nodes do not depend on their $k$-core index, which instead determines whether or not a given node prevents the diffusion of a rumor to a system-wide scale. Our findings are relevant both for sociological studies of contagious dynamics and for the design of efficient commercial viral processes.
I. INTRODUCTION
The paper examines influential spreaders in rumor dynamics, asking whether k-core position identifies privileged spreaders as it does in epidemic models. It uses rumor spreading to study information dissemination across social and communication contexts.
- Motivation: Rumor dynamics is relevant to information dissemination, including viral marketing and collective social mobilization.The paper connects rumor-like mechanisms with spreading news, opinions, protest messages, and commercial viral processes.
- Research question: The study identifies influential nodes dynamically by their role in disseminating information, rather than by authority or hierarchy.This perspective focuses on nodes with outstanding dissemination roles in a network.
- Research question: The paper tests whether k-core index, previously associated with epidemic spreading capacity, also identifies privileged spreaders in rumor dynamics.The introduction explicitly contrasts the epidemic result with the question posed for rumor models.
- Approach: Extensive simulations are conducted on real-world communication networks ranging from roughly 10^3 to almost 10^5 nodes.The networks are used to evaluate rumor spreading across substantially different system sizes.
II. DATASETS.
The study uses several real-world communication networks, including email, political blogs, autonomous systems, and Twitter, and characterizes their nodes by k-core index.
- Datasets: The simulations use email, political-blog, Internet autonomous-systems, and Twitter networks as real-world communication datasets.These networks represent reciprocal communication, hyperlinks, physical connectivity, and follower relations, respectively.
- Email contact network: The email contact network contains 1133 nodes in its giant connected component, with average degree ⟨k⟩= 9.6.Nodes are email accounts, and links represent exchanged emails.
- Political blogs network: The political blogs network contains 1222 nodes in its giant connected component, with average degree ⟨k⟩= 27.3.Its directed links represent hyperlinks between weblogs on U.S. politics.
- Autonomous-systems network: The largest connected component of the autonomous-systems network contains 33235 ASs, with average degree ⟨k⟩= 4.5.Nodes are autonomous systems connected by physical links.
- Twitter network: The Twitter dataset contains 87569 users participating in Spanish May 15th protests, with directed follower relations.Incoming links indicate users a node listens to, while outgoing links indicate users paying attention to it.
- Network characterization: The k-core procedure recursively removes vertices with degree less than k, and higher coreness places nodes closer to the network nucleus.Here degree is defined as k = k_in + k_out.
III. RUMOR DYNAMICS
The rumor model divides nodes into ignorants, spreaders, and stiflers, with transmission occurring through spreader–ignorant contacts and termination through stifling.
- States: Each node is an ignorant, spreader, or stifler, representing respectively an unaware node, an active transmitter, or an informed non-transmitter.Their densities are ψ(t), φ(t), and s(t), which sum to 1.
- Transitions: When a spreader contacts an ignorant, that node becomes a spreader at rate λ.Rumor propagation therefore occurs along links connecting spreaders and ignorants.
- Transitions: A spreader becomes a stifler at rate α after contacting another spreader or stifler.Repeated unsuccessful communication attempts can also end a node’s spreading activity.
- Process variants: The contact process lets each spreader contact one randomly chosen neighbor per time step, whereas the truncated process contacts all neighbors until stifling interrupts further contacts.The two versions differ in how many neighboring contacts each spreader attempts.
IV. RESULTS
The results quantify rumor penetration by averaging final stifler density across repeated simulations for every possible seed, then grouping seeds by degree and coreness.
- Simulation protocol: Each node serves as the initial seed in repeated simulations, with 10^3 runs for the smallest networks and 10^2 for larger ones.The resulting averages provide statistically significant estimates while accounting for computational costs.
- Spreading capacity: A node’s spreading capacity is measured by the average final stifler density when that node initiates the rumor.The measure indicates how deeply the rumor penetrates the network from that seed.
- Grouping seeds: Seeds are coarse-grained into classes according to degree and k-core index to compare their average rumor outcomes.The analysis separately groups nodes by k-core index and by joint degree–coreness values.
- Grouping seeds: The study averages final stifler density over nodes sharing the same degree and k-core values.This joint grouping enables comparisons among nodes with matched topological descriptors.
A. Spreading capability
Rumor spreading capability is nearly independent of a seed node’s coreness, but coreness determines whether central nodes become critical firewalls that halt diffusion.
- MkS is almost invariant across the seed node’s core number, indicating that spreading capabilities are nearly the same throughout the network.
- Across the tested rumor settings and networks, no correlation appears between average stifler density and seed centrality, regardless of α.
- Nodes in the highest core become stiflers earlier than nodes elsewhere, forming topological barriers to rumor expansion.
- Within the highest core, stifler time generally decreases as node degree increases, except for a small fraction in the CP setting.
- The absence of influential spreaders is therefore accompanied by critical firewalls whose existence depends on node coreness.
B. Awareness of information
Rumor dynamics distinguish spreading from awareness: central nodes often hear many rumors and become stiflers, allowing them to filter or short-circuit further dissemination.
- Critical nodes may filter information and coordinate collective action, acting as enhancers in some cases and firewalls in others.
- Centrality is usually sufficient for a node to hear at least half of the simulated rumors, while high-degree nodes hear most rumors through their many incoming paths.
- Coreness is a better descriptor than degree for estimating whether a node ends in the stifler class after rumor spreading.
V. CONCLUSIONS
Across four real-world communication networks, rumor spreading shows no privileged influential spreaders: spreading capacity is largely seed-independent, while central nodes instead act as rumor firewalls and information sinks. High-coreness nodes commonly become aware of rumors before they die out, giving them an awareness advantage.
- The study tests rumor dynamics on four real-world communication networks as an alternative to epidemic-based analyses of influential spreaders.It uses two rumor-dynamics versions and extensive numerical simulations.
- Rumor spreading does not favor influential spreaders because the final fraction of stiflers is similar regardless of where the rumor starts.The spreading capabilities of different nodes are almost the same across seed locations.
- Central nodes are important as firewalls rather than dissemination enhancers, with high k-shell or degree nodes becoming stiflers quickly and interrupting information propagation.Their short transition time to the stifler state helps choke spreading at early times, regardless of the seed.
- Figure 3 shows that nodes with low degree but mid-to-high coreness are systematically reached by roughly any generated rumor, regardless of its origin.Awareness above 50% is represented by white-to-red colors across the four networks.
- Because central nodes act as rumor firewalls, high-core nodes often hear rumors before they die out and therefore gain an information advantage.Their advantage is awareness of information circulating throughout the network, not superior rumor dissemination.
- The conclusions motivate more realistic rumor dynamics using online-social-network data on how information is generated, exchanged, forwarded, or banned.The authors present this as a direction for improving understanding of information phenomenology.