Wherefore Art Thou R3579X? Anonymized Social Networks, Hidden Patterns, and Structural Stenography

A social network occurs anywhere there is social interaction between people.

Examples include Email, instant messaging, Facebook, blogging trackbacks, coauthor networks

The structure of social networks can be interesting

How are friendships usually structured? Are there hubs, such as Heather, who connect separate networks? How many degrees of Kevin Bacon?

We can investigate these questions if we have the data to mine.

For our examples, we will use a network of emails sent between users.

How do we protect users’ privacy while still releasing the data for research?

John Mary

Vertex VertexDirected edge

Remove any identifiable information, such as name and other attributes.

Randomly rename the vertices

R3579X R73313

Convert directed edges to undirected edges. This increases the complexity and makes it harder to attack.

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Undirected edge

Let’s say you want to know if two vertices are connected onthe graph.

All the identifying info has beenremoved, so how do we do it?

An active attack involves the adversary creating vertices in the graph before the graph is released

The adversary will create edges between the vertices in a fashion that it can then recognize later on in when the graph is released

We create k new vertices around 2*(log n) where n is the total number of vertices

We create new do – d1 edges between these new vertices and the other ones in the graph

Then, we randomly create edges between these new nodes with independent probability of 1/2

Given the graph, how do we find the subgraph that we created?

Create a search tree, pruning the tree based on the properties of our subgraph, such as the number of degrees of our new vertices

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The paper proves that the search tree does not grow too large and that the algorithm displays good performance

Also, it proves that the subgraph is unique so that we don’t identify the wrong subgraph

They simulate an attack on LiveJournal friendship links. They create the accounts on the website, make the connections, and then crawl the site and anonymize the data

The network has 4.4 million nodes and 77 million edges

Only needs sqrt(log(n)) new nodes to attack the graph

However, it’s much more computationally intensive and less practical in the real world, although it takes less nodes

It’s a lot like an active attack, except you don’t create new nodes, instead you collaborate with your friends and find yourselves in the graph

However, because you did not specifically target certain people, you may not be able to identify other people when you find yourself

We cannot rely on anonymization to ensure privacy in social networks

Possible improvements: add noise to the data by adding/removing random edges