When trying to grow and deepen online relationships, actions should be grounded in an authentic intent to add value to your audience.

7 Simple Ways to Grow and Deepen LinkedIn Relationships

Provide thoughtful insights and questions on contacts' LinkedIn posts and updates to foster an exchange and engagement.
Like and share contacts' LinkedIn posts, updates and promoted content to LinkedIn.
Personalize congratulatory notes on professional milestones.
Proactively visit the profiles of contacts and endorse them for relevant skills and expertise, not just the attributes that populate at the top of their profile.
Visit your contacts' 'Contact info' section and follow them on other social channels to deepen your understanding of the contacts' interests and passions.
Publish blog content as LinkedIn posts that relates to the interests of your contacts and network and share it with them via LinkedIn messaging.
Share your published LinkedIn posts in relevant industry groups and ensure your content title and summary create interest in reading further.

It is also critical that these actions become part of your regular cadence of networking activity and form a habit. Find and schedule time in your day to ensure adoption of the change.