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About the Author:
Harsh Modi is internet marketer and also writes article on outsourcing projects, data entry outsourcing, outsource web 2.0 development, iphone development etc.

Networks are one of the most explored structures in computer science because they have applicability in many different scenarios. A number of algorithms have been devised for these structures; one of the most entertaining results is the so-called Bacon number: a measure of how close a particular actor is to Kevin Bacon in the world of film.

This comes from the popular trivia game that has long been played in pubs around this great nation: the ‘Six Degrees of Kevin Bacon’. Here’s how it works: someone names an actor and then everyone has to try and work out the number of steps (‘degrees of separation’) between that actor and Kevin Bacon. The result is the Bacon number. Everyone who has worked directly in a movie with Kevin Bacon has a Bacon number of 1 (Kevin himself is assumed to have a Bacon number of 0). Those who have worked with one of those people will have a Bacon number of 2, and so on.

So, for example, suppose someone says ‘John Thaw’. John Thaw never appeared in a movie with Kevin Bacon, but he did appear in Chaplin alongside Diane Lane. In turn, she appeared in My Dog Skip with, you guessed it, Kevin Bacon. Hence John Thaw has a Bacon number of 2. (There may be other links between John Thaw and Kevin Bacon of degree 2, but the prize goes to the first person to suggest the shortest link, and hence the smallest Bacon number).

There’s a great website called The Oracle of Bacon that periodically downloads data about movies and their casts from the Internet Movie Database to refresh its own database. From this data it builds a big map of actors and movies and can answer these kinds of degrees of separation questions. (Quick aside: what’s the shortest link between Billie Piper and Sean Connery? Apparently she had a bit part in Evita alongside Mark Ryan, who was in First Knight with Connery. A ‘Connery number’ of 2 for Billie Piper, then.)

It’s a small world

In mathematics there’s a similar concept known as the Erdös number, which is named after the prolific Hungarian mathematician Paul Erdös. He published a massive number of papers with many collaborators across many disciplines. The Erdös number for an academic is the number of steps between Erdös and themselves, via collaborators on papers. So Paul Erdös would have an Erdös number of 0, all of his collaborators on the various papers he wrote would have an Erdös number of 1, and all their collaborators on other papers would have an Erdös number of 2, and so on.

All of these degrees-of-separation-type numbers are based upon the small world phenomenon. This is the observation that the social networks of large groups of people in modern society are very interconnected. Typically, they’re distinguished by short path lengths between any two nodes.

The psychologist Stanley Milgram did some research on these social networks during the ’60s and found that, on average (and using the methodology he described), any person in the US could trace a path to any other person in the US using between five and six links. Hence the term ‘six degrees of separation’, although Milgram did not use this particular phrase (it was first widely used as the name of a play and then a film – the star of the movie was Will Smith, who has a Bacon number of 2).

The small world phenomenon is of course widely used nowadays by the social networking sites such as Facebook and MySpace, although it’s best known as part of LinkedIn, where you can view your network separation from another person directly.

Meet the neighbours

So how are these degrees of separation worked out? How does the Oracle of Bacon calculate the shortest number of links (the path) between actor A and actor B?

Graph theory holds the answer. Not graphs in the sense of those diagrams you had to draw at school to show y=x2, but computer science graphs, or networks. The algorithm used is a ‘shortest path’ algorithm.

First, we need some terminology. I’ve already let slip a few pieces of jargon, so let’s be more rigorous. A network is a data structure consisting of nodes (sometimes known as vertices) and the edges that connect the nodes. You can most easily represent a network as a matrix, though this is inefficient in terms of memory. Each row and column represents nodes, and the intersection of a row and column will be 1 (or ‘true’) if there’s an edge between the nodes represented by the row and column, and 0 (or ‘false’) otherwise. Sometimes the edges have a ‘weight’ associated with them, which is the value in each cell. (An example of this is a network of towns, where the weight of the edge for two towns would be the length of the most direct route between them.)

A path is a set of edges using which we can travel from one given node to another. The length of the path is either the number of edges we have to travel to follow the path, or the sum of the weights of the edges. The shortest path is obviously the path with the smallest ‘length’.

Suppose we have a network, as shown in Figure 1 above. We want to find the shortest path from A to B. We’ll first consider the simple case where the path length is merely the count of the number of edges we follow.

We’ll need to store some information for each vertex we visit, so we should first create an array that stores references to all the nodes in the network. We’ll get to the information we need to store in a moment, as we describe the algorithm. We’ll also need an implementation of a ‘queue’ to hold nodes we’re about to visit.

Our algorithm uses a technique called ‘breadth-first’ search. In it, we visit all the neighbours for a vertex before visiting the neighbours themselves, and so on. It’s rather as if the search ‘fans out’ from the original node. The alternative search technique is known as ‘depth-first’ search, where we explore the nodes by following edges as far as we can go, and then backtrack to follow the edges that we missed.

Back to the breadth-first search. Set the first node’s ‘path length’ to 0. That’s the first value we have to store with each node in our array (obviously, the first node is at distance 0 from itself). Add the starting node to the queue. Now, in a loop, continue removing nodes from the queue until we find the target node. For each node we pick off the queue, mark it as ‘visited’ (to do this we’ll need a second value – a true/false indicator – and all nodes should be marked as unvisited at the start). Then add all the nodes immediately reachable from that node to the queue.

However, there’s a quick test here: there’s no point in adding nodes that have already been visited, since if they are being visited again, the new path length must be longer than before. Also, when you add the neighbour nodes to the queue, set their path length to one more than the current node’s path length.

You stop when you pick off the target node from the queue. Its path length value will be the shortest distance from the source node to the target node.

Weights and measures

If you also want to output the path taken from A to B, you should record the ‘parent’ of each node as well as its path length when you queue the node (the parent is the node from which you’re following the edge). Once you reach B you can follow the path back to A by following the parent links. (If you want the path in the right order, merely push the nodes on to a stack as you go back to A, and then you can pop them off in the forward order.)

Figure 2, above, shows this algorithm in action by colouring the edges visited at each step and the contents of the queue at each stage. Step 5 is the interesting one, since the edge marked in blue/grey is not followed (because the node at the end of it has already been visited).

For our application to Bacon numbers, the network may be huge (lots of nodes – sorry, actors – with each actor having many links to other actors), but this algorithm will suffice.

For the other kind of network where each edge has a weight associated with it, the algorithm changes slightly, although it is still based on the idea of breadth-first search. Here, we’re going to find the path that has the smallest cost (that is, the smallest total weight). We could find, for instance, that such a path has more edges than a strict ‘shortest’ path would have. This variant on the shortest path algorithm was first devised by Edsger Dijkstra (the computer scientist who published the well-known paper called ‘Go To Statement Considered Harmful’ in 1968 that lambasted the then common and prolific use of the Goto statement in programs).

The big assumption here is that all the weights are positive numbers. The reason for this stipulation is that if an edge has a negative weight, and that edge forms part of a cycle of negative length, you could travel round the cycle ad infinitum to produce shorter and shorter (more and more negative) paths.

Instead of an ordinary queue, Dijkstra’s Algorithm makes use of a priority queue. A priority queue is usually described as a queue to hold items from which you always pick off the item with the highest priority (and is so used in operating system job queues or printer queues), but can apply to any set of items from which you want to pick off the smallest or the largest. We’ll use the variant, where the next item you remove from the queue at each stage will be the smallest.

We start off as before: set the path length (or cost) to 0 for the first node, and add it to the priority queue. Now we loop over the queue, picking off nodes until we find the target node (and we will pick off the smallest node at each step). For each node we remove, however, we do some extra work. As before, we have to mark nodes as visited or unvisited (and obviously mark all nodes as unvisited at the start). When we remove a node from the queue, it is marked as visited.

For the current node, we look at each of the nodes reachable from it. If a neighbour node has been visited, we ignore it, much as we did before. For the other neighbouring nodes, we calculate the total cost to reach them from this one. Say the current node has cost 10, and the edge to another node has cost 4. The cost of the next node is therefore 14, through this particular node. Check whether this is less than the current cost of the next node (for this to work we shall have to set the cost of all the nodes – except the first – at the start to some very large number, usually called infinity). If it is, update the cost of the next node with this new smaller value and store the current node as its parent. Note that this will probably put the next node in a new position in the queue.

Completing the network

Once we remove the target node from the priority queue, we’ll have, as before, a path from it back to the original node, and we’ll also have the cost of that node as accumulated from the source node.

Figure 3, above, shows an application of Dijkstra’s algorithm to a simple network. Step 1 is the original network, and each of the edges is marked with its weight. Step 2, we start at A and find the smallest edge (the one with weight 1). That defines the next node to become our starting point for Step 3. Actually, for Step 4 we have two possible nodes of weight 3: the one in the middle and the very bottom one. For brevity, I chose the middle one so that the algorithm completes with Step 4 at B. The shortest path is the one marked.

Traditionally it was employers who had to make themselves visible when looking to fill vacancies – posting adverts in the press, then choosing a pool of candidates from a veritable tsunami of applicants. But not any more. There’s mounting evidence that personnel specialists are now scouring social media sites and job boards for potential employees.

“Recruitment departments are starting to dabble with professional networking and other forms of social media to head- hunt potential candidates,” says Teresa Sperti of The IT Job Board. Microsoft recruiter Declan Fitzgerald claims that he saved £60,000 in recruitment fees by sourcing nine programming posts through professional networking site LinkedIn instead of using traditional channels.

That’s all good news if you’re currently looking for a job in IT. What better way to ply your wares than on the web, where you can track down the right people and demonstrate your expertise direct? Consider this your ten step guide.

Step 1: Set up multiple accounts

The first rule of successful professional networking is to keep business and pleasure strictly separate. Multiple social networking accounts will help you to present your best face to recruiters. A good first step is to use business-oriented networks like MySpace and LiveJournalfor mates. However, with Facebook and Twitter accounting for the lion’s share of media attention and internet traffic, that approach will exclude access to a lot of influential contacts. Setting up two separate accounts for friends and business on these networks will enable you to compartmentalise your image.

To stop all these accounts getting out of control, use tools that are capable of managing more than one account. Both TweetDeck and Twhirl let you post to more than one Twitter account without the need to continuously log in and out. Seesmic Desktop does the same job, and it handily also allows you to update your Facebook status at the same time.

Step 2: Use Facebook’s privacy settings

While it’s good practice to create business profiles on business-oriented social networks, Facebook is the undisputed hub of the net’s social activity. So, here’s an alternative to multiple profiles: tweak Facebook’s privacy settings so that work contacts aren’t able to see any of your friends’ pictures of your latest debauched night on the town.

Click ‘Friends’ on the main menu bar in Facebook and then click ‘+Create’ in the Lists section of the sidebar. Call this list ‘Work’. You’ll be given the option to add existing friends to this list. Create a second list called ‘Mates’. Once created, you can add anyone who requests friendship to either list.

To make people on your Work list see a professional-looking profile, go to ‘Settings | Privacy | Profile’. The options here allow you to choose exactly who sees what. As an example, let’s say you only want people on your Mates list to see your photos. Click on ‘Edit photo album settings’, choose an album and make sure only your friends can see it. Then, in the ‘Except these people’ box, type in ‘Work’. Now you’ll be able to share all the amusing photos you want to with your mates, safe in the knowledge that the people on your ‘Work’ list can’t see what you get up to after hours.

Step 3: Be careful what you say

Separating your work and personal lives is only one part of the process of creating a professional image for yourself online – a technique named ‘personal branding’. You need to present a ‘best version’ of yourself using the whole range of social-media tools available.

“My key Twitter advice to BBC colleagues (is) don’t say anything you wouldn’t say on air,” BBC Technology Correspondent Rory Cellan Jones recently tweeted. That advice holds true whether you’re blogging, tweeting or changing a public Facebook status update.

“It is very easy to build your reputation and credibility using social media. Unfortunately, it’s just as easy to damage it irrevocably by being careless and whimsical in its use,” says Judith Germain, Managing Director of leadership consultancy Dynamic Transitions. “One thing to remember is that everything that you do on the web is permanent, even in ‘closed’ networks.”

The website Tweleted and the Google cache mean that even deleted posts can be easily found. So think for a second before pressing that ‘Update’ button. And if you do find yourself participating in an argument, make sure you’re polite – or just anonymous.

Step 4: Promote your expertise

Establish yourself as an expert in a particular field or subject. Social-media sites offer plenty of opportunities to promote yourself as a leading light in your area. LinkedIn’s Answers application is a great place to put this into practice. Browse through questions that other LinkedIn members have posted in your area of expertise or search by keyword. The more good-quality answers you provide, the more visible you become.

If you’re willing to invest more time, consider joining Experts Exchange, a site where people post IT related queries. Join as a volunteer and accrue points towards ‘expert’ status through providing solutions.

Blogging is another possibility, but be careful. Post expert advice and considered opinion rather than your opinion on Alton Towers or the prices at Starbucks if you want to draw a returning crowd. A post called ’10 Things To Do If Your PC Crashes’ is worth much more than a whining rant about Windows being buggy.

Step 5: Don’t be a spammer

Blog articles with titles like ‘10 Reasons I’ll Un-follow You on Twitter’ cite aggressive self-promotion as the fastest route to lose friends and alienate people, so avoid things like pushing your website with every status update or spamming hashtags with inappropriate information just to get yourself noticed.

The key to keeping followers and impressing recruiters is to balance your activity. “Engage with your network,” says www.mashable.com contributor Atherton Bartleby. “Genuine engagement with your followers will ultimately ensure that your mobile number is retained and not ‘lost’ at the end of that fabulous party, and it will ensure that you don’t (too often) commit any serious faux pas.”

Step 6: Follow the right folks

Here’s a great tactic to ensure you make the right contacts: put together a list of companies you’ve got in your sights, find out who works there and, if possible, who’s in charge of hiring. Then make friends with or follow them on social-networking sites. Some corporate sites list personnel in their ‘About Us’ section – so try that avenue first. Search LinkedIn for company names if you hit a brick wall with the first method, and back that up with a search of PeekYou, Plaxo and Spoke. These are all social media directories aimed at business users. A multipronged approach like this should yield a lot of names – and you can make friends with people on all these networks.

Once you have concrete names, search for them on Twitter and Facebook. Click ‘Find People’ in Twitter, then enter first name and last name as keywords to find everyone registered under that name. Facebook is trickier – a name search may pop up a bigger list of false positives – so search by email address instead.

If you haven’t found anyone in your initial search, try a people directory like Pipl – a search engine that specialises in digging up data from ‘the deep web’, including social network profiles and blogs. This will also reveal other social-media sites your target is signed up with. Finally, use Google Blog Search to track down your target’s blogs – and when you can comment on a post, do it.

Step 7: Join specialist groups

Don’t just rely on your virtual friends for leads – join specialist groups and communities online to get an inside track and promote your expertise. Even mainstream social-networking sites have a lot to offer.

“Look to existing networks, such as Facebook and LinkedIn, where there will be groups that discuss the industry and specific technologies and practices within it as well as dedicated forums and communities for the sector,” says Rachel Hawkes, one of the brains behind Social Media Portal. “The IT specialist should look to become engaged with the communities and establish a presence that adds value to the other community members by offering opinion, advice and leadership.”

Doing this properly requires some commitment, though. To get the best from specialist groups, you should check in and post regularly. It’s sensible to follow the old school rules of ‘netiquette’ when joining any new group. Lurk for a while and get a feel for the tone of conversation before you join in with a comment. Some groups may require you to post an introductory note, for example. Others may frown on long, self-promotional signatures.

It’s worth searching out specialist communities that match your expertise outside of the obvious choices, too. As an IT specialist, you’ll find social networks running on message boards, mailing lists, Yahoo Groups and Google Groups.

Step 8: Do a job search

Once you’re hanging out in the right online neighbourhood, you’ll hear about some of the best jobs going. That doesn’t mean you have to stop being proactive, though.

“In a recent survey we conducted, when asked which tools they considered most important when applying for jobs, 40 per cent of IT candidates referred to using skills-specific job boards and 32 per cent said they would make direct contact with a company,” says Teresa Sperti of The IT Job Board. ”Seasoned or specialist IT professionals candidates often favour skills-specific job boards, with only four per cent of candidates seeing generic job boards as very important to their job search.”

In other words, using sites that cater specifically to your area of expertise pays dividends. At The IT Job Board – and most other sites – you can sign up for an email summary matching a keyword search. A great way to keep tabs on job sites is an RSS feed, which is easy to add to your iGoogle front page or check in your favourite feed reader. For example, search by keyword at job site Computing Careers and you’ll find an RSS feed link at the bottom of your returned results.

Step 9: Make a video resume

Hopefully your efforts at making yourself visible in a good way to the right people will not have gone unnoticed, and your name will start to surface when positions need to be filled. If that’s the case, you need something more than your various social-network profiles to surface when somebody Googles your name. Owning a website is an obvious first step, but another idea that is gaining momentum at the moment is the video resume.

Thousands of people have posted CVs on YouTube, although the quality is highly variable. If you can’t afford professional production costs, keep things simple. Use the best quality camcorder you can, and make sure the lighting’s natural. Record sound separately, using a decent condenser microphone if possible. You can do the latter directly into Audacity, an open-source sound-editing tool. Many of the best video resumes feature a fixed shot of the subject talking about themselves to camera, but it’s still fine to use software like Windows Movie Maker to add photos and clips too.

Though making a video resume is still a fairly new idea, it’s catching on as a trend – so you’ll have to work a little bit harder to come up with something that stands out. Mike Anderson’s produced his CV in graph form – and got to the front page of Digg and almost 200,000 hits on Flickr. Then there’s Australian games designer Jarrard Woods, who launched his freelance career by building his Super Mario Bros resignation.

Just remember: this clip from the comedy series How I Met Your Mother is intended as a parody (specifically of this infamous disaster), not an inspiration. But you can try this style too if you like.

Step 10: Measure your impact

Keeping up a presence on lots of sites can be a drain on your time – so measure your success with people by measuring traffic from each site, then ditch the ones that don’t work. You can use web analytics tools like Webalizer and AWStats to see where hits to your blog or online CV are coming from. Both programs summarise referrer sites in tables for you – but there’s a lot of static to work through.

A more effective method is to encode URLs you tweet or place in social profiles with a shortening service like Bit.ly. Every time you post a shortened URL, Bit.ly will track how many clicks it generates. Create a different version of the URL for each of your social networks and you can instantly see which work best.