Source-linked AI summary
Local structure can identify and quantify influential global spreaders in large scale social networks
Yanqing Hu, Shenggong Ji, Yuliang Jin, Ling Feng, H. Eugene Stanley, Shlomo Havlin
TL;DR
Measuring node influence in large social networks is challenging when the full network structure is unavailable. The paper uses percolation theory to relate local spreading behavior to influence; it reports that local structure can quantify influence and that its seed-selection approach gives nearly optimized solutions.
Problem
Quantifying and optimizing node influence in huge social networks is challenging when the full network structure is unavailable.
Source: Method · p. 1Method
Using percolation theory and the SIR model, the paper estimates individual and collective spreading power from local infection clusters and applies a greedy seed-selection algorithm.
Source: Result · p. 1, Method · p. 4Results
Local network structure suffices to quantify node influence, and PBGA is reported to give nearly optimized seed sets across the considered numbers of spreaders.
Source: Summary · p. 6, Method · p. 6Takeaways & Limitations
The authors suggest the approach may support false-information surveillance and control, viral marketing, epidemic control, and network protection.
Source: Method · p. 1The method focuses on a subset of candidate nodes rather than selecting seeds from the whole network.
Source: Method · p. 4
Abstract
from arXiv · showhide
Measuring and optimizing the influence of nodes in big-data online social networks are important for many practical applications, such as the viral marketing and the adoption of new products. As the viral spreading on social network is a global process, it is commonly believed that measuring the influence of nodes inevitably requires the knowledge of the entire network. Employing percolation theory, we show that the spreading process displays a nucleation behavior: once a piece of information spread from the seeds to more than a small characteristic number of nodes, it reaches a point of no return and will quickly reach the percolation cluster, regardless of the entire network structure, otherwise the spreading will be contained locally. Thus, we find that, without the knowledge of entire network, any nodes' global influence can be accurately measured using this characteristic number, which is independent of the network size. This motivates an efficient algorithm with constant time complexity on the long standing problem of best seed spreaders selection, with performance remarkably close to the true optimum.
Result
SIR spreading has distinct local and global outcomes, separated by a characteristic infection size. The local phase supports accurate influence measurement and seed selection using local network structure.
Result
- The local characteristic infection size s∗ determines the key influence size in the stochastic SIR-family spreading process.SIR-family models are described as models of information spreading in social media.Source: Result · p. 1
- In the supercritical regime, spreading either reaches a finite fraction of the population or quickly diminishes beyond the local characteristic infection size.The two phases are unambiguously separated, and global spreading occurs irrespective of the initial condition.Source: Result · p. 1
- Local-phase statistics can accurately quantify node spreading power and support best-seed selection using local network structure in constant time.The method uses statistical properties of infected-cluster sizes.Source: Result · p. 1
Method
The method maps SIR spreading to percolation and uses a characteristic local size to distinguish contained outbreaks from viral ones. It truncates influence estimates at that scale and applies them in a greedy seed-selection algorithm.
Method
- The spreading-size distribution has separated local and viral peaks, allowing a small filtering size to distinguish the two outcomes.The viral peak is centered at a size independent of the seed node and stochastic realizations.Source: Method · p. 2
- Maximizing spreaders is equivalent to maximizing influence that also includes listeners, because both totals increase monotonically with the number of spreaders.Listeners are nodes linked to spreaders that do not spread the information further.Source: Method · p. 2
- For m ≥ s*, truncated spreading power approximates exact influence with controlled error; the relative error becomes negligible at this threshold.The error decreases quickly with m.Source: Method · p. 3
- At s∞ = 0.3N, the influence radius is about 3–4 steps across studied OSNs; local spreading vanishes within that distance, otherwise it reaches about 0.3N nodes.The radius is smaller than the networks’ average distance and diameter.Source: Method · p. 3
- Truncation reduces single-node influence computation from linear growth in N to O(m), independent of network size.The authors report PBGA execution count is independent of N.Source: Method · pp. 3–4
- PBGA greedily selects seeds by maximizing marginal gain in truncated collective spreading power over a candidate set.It first selects the strongest individual spreader, then repeatedly adds the seed that maximizes the collective estimator.Source: Method · pp. 3–4
- For small seed sets, PBGA is indistinguishable from the brute-force optimum and significantly outperforms MCI; the difference diminishes as M increases.The figure compares the ratio of the seeds’ influence for PBGA and MCI.Source: Figure 4 · p. 4, Method · p. 5
- A PBGA solution found at β0 performs nearly optimally at higher β when both rates are above βc.The authors suggest choosing a rate slightly above the critical value when the actual rate is unknown.Source: Method · p. 6
Summary
The paper argues that a node’s influence can be quantified from its local network environment, based on spreading dynamics. It distinguishes this from local approximations that cannot quantify actual influence and identifies conditions for broader applicability.
- Any node’s influence can be quantified purely from its local network environment, based on the nature of the spreading dynamics.Source: Summary · p. 6
- Unlike distance-truncation approaches that approximate relative global measures, this framework quantifies actual influence.Source: Summary · p. 6
- Beyond basic SIR, applicability requires localized or global outbreaks and a global influence size uncorrelated with the initial spreader.Source: Summary · p. 6