Final answer:
Eigenvector centrality is important for spreading and innovation because it indicates both direct and indirect influence within a network, suggesting that well-connected individuals or organizations can have greater impact in disseminating new ideas.
Step-by-step explanation:
Eigenvector centrality is useful in the context of spreading and innovation because it implies that a node's importance is not just a function of its direct connections, but also of the the importance of those it is connected with. This metric effectively captures both direct and indirect influence within a network.
When considering the spread of innovation, a node (individual or organization) with high eigenvector centrality is not only directly connected to many others but is also connected to nodes that themselves are well connected. This amplifies the potential for an innovator's work to have significant reach and impact. The more central a node is in a network, the more likely it is to receive and disseminate new ideas, leading to a wider spillover effect.
As the question hints, the social benefit of an invention is greater when its influence can spread through central nodes in a network, thereby reaching a larger audience and creating broader impact. Eigenvector centrality provides an incentive for innovation by highlighting the importance of well-connected nodes in the diffusion process and reassuring the innovator of a wider dissemination and adoption of their invention due to the interconnectedness of significant nodes.