Gene

Combinatorics

Physics

Data mining

World Wide Web

Function (biology)

Asynchronous communication

Repressor

Economics

Operator (biology)

Topology (electrical circuits)

Acoustics

Relation (database)

Degree (music)

Convergence (economics)

Index (typography)

Scale (ratio)

Measure (data warehouse)

Computer network

Mathematics

Computer science

Economic growth

Genetics

Quantum mechanics

Node (physics)

Transcription factor

Biology

Nature Communications

Identifying influential nodes in dynamical processes is crucial in understanding network structure and function. Degree, H-index and coreness are widely used metrics, but previously treated as unrelated. Here we show their relation by constructing an operator , in terms of which degree, H-index and coreness are the initial, intermediate and steady states of the sequences, respectively. We obtain a family of H-indices that can be used to measure a node's importance. We also prove that the convergence to coreness can be guaranteed even under an asynchronous updating process, allowing a decentralized local method of calculating a node's coreness in large-scale evolving networks. Numerical analyses of the susceptible-infected-removed spreading dynamics on disparate real networks suggest that the H-index is a good tradeoff that in many cases can better quantify node influence than either degree or coreness.

The H-index of a network node and its relation to degree and coreness