Hey borja! I have had terrible experiences trying to visualize large graphs on neo4j in the past. I highly recommend that you export the graph to other formats and use tools such as Gephi to visualize. https://gephi.org/ 

Here are few resources from my notes on that topic:

It really depends on what aspects of the network you want to visualize. Here are few resources to check:

1.       Free/ Open Source Software

• Gephi - https://gephi.org/ - Open Graph Viz. Software - check how to do edge bundling
• Pajek - http://mrvar.fdv.uni-lj.si/pajek/ - Large network vis tool
• Cytoscape - http://wiki.cytoscape.org/
• D3 in R - http://christophergandrud.github.io/networkD3/

2.       Interesting Approaches

• Biofabric - http://www.biofabric.org/ - displays a network where nodes are depicted as horizontal lines, not as points. Edges are then shown using vertical line segments.
• Mike’s Circos and Hive Plots - http://mkweb.bcgsc.ca/psa/circos.hiveplot.pdf

3.     Try out Key Lines form Cambridge Intelligence https://cambridge-intelligence.com/ - interactive

We analyzed 700 GB of entire world's OpenStreetMap data, as well as its user community networks. We effectively show the underlying structure, we used head/tail breaks: Article Characterizing the Heterogeneity of the OpenStreetMap Data a...

Use 'Open Graph Viz Platform' https://gephi.org/

D3.js is a great library for any kind of data visualization including graph structures.

https://d3js.org/

you can use D3.js or Dc.js which is created on top of D3.js, it should be easier and it offers graphs too ..

you can check here an example :

http://dc-js.github.io/dc.graph.js/random.html

the library :

https://github.com/dc-js/dc.graph.js/