There is a theory that in this interconnected world, any two people can be connected by just six acquainted links or less. While this concept is famous for exploring the prolific film career of actor Kevin Bacon, the theory is actually a complicated 87-year-old computational mathematics problem that later took more than 20 years to prove and went on to serve as the basis of modern social media. In more practical terms, “Six Degrees” – or the “small world theory” – suggests that everything and everyone in this world is connected to one another in a meaningful way.

Fanatics decided to put this theory to the test by examining how separated NBA players who have played on the same team are from one another. Check out our methodology to see that while players who played in the same season would be connected by relatively short degrees chains, the chain of acquaintances between modern players and Hall of Famers may be significantly more complicated.

What do the networks of some of basketball’s greats look like? Check out the connections of Michael Jordan, Kobe Bryant, Kevin Garnett, and LeBron James.

The Current NBA Player Constellation

The image above is a node graph showing the interconnectivity of every NBA player either currently playing today or who has recently played in the league. While not every player would have played with every other one in the league, the graph is still relatively complicated. The majority of players would have direct links with each others due to trades, interdivisional play, or inter-conference games.

The larger dots represent “good hubs,” where there are a large number of connections. For example, Dirk Nowitzki has 162 connections and Paul Pierce has 177. The larger a dot on the graph, the more connections it has and the “better” the hub is. The small dots on the periphery of the graph represent players who have only one connection, due to being injured, being cut early from the team, or being retired and having a connection with a player who is still active.

The NBA Family

Every NBA Player Since 1947

The graphic above represents every player who has played for the NBA since the second season of the league’s predecessor – the Basketball Association of America (BAA) – in 1947. As is expected from such a query, the node graph is a linear chain, where connections are most likely to exist only with the nodes next to it. As a visual representation of the league’s history, the graph reveals a shared heritage among those who played in the league, which is inherited and passed on from generation to generation.

The graph also shows how the league’s various contractions and expansions have affected the players’ connections. For example, the integration of the American Basketball Association (ABA) in 1976 increased the constellation of players, as did the expansion drives of 1988 and 1995 – the second of which saw the NBA expand into Canada.

Of note is the fact that as the graph moves closer to the modern day, it grows less dense. This is because as the league grew larger, the likelihood of players playing with each other grew fainter.

Getting Around

Some players have played with more players than others, making them better “hubs.” Juwan Howard, for example, who is currently an assistant coach with the Miami Heat, played six and a half seasons for the Washington Bullets/Wizards, three seasons for the Houston Rockets, and three seasons for the Miami Heat, and had stints with the Dallas Mavericks, the Denver Nuggets, the Orlando Magic, the Charlotte Bobcats, and the Portland Trail Blazers. The length of his career, combined with the number of teams he played for, makes Howard the largest “hub” on the NBA node graph, with 264 connections.

Other major hubs include Joe Smith at 257 connections – Smith played for 12 different teams over his 16 years career – and George Johnson at 255 connections. Johnson played 13 seasons with the league and played for six different teams. Finishing the top 10 are Jim Jackson, Kevin Willis, Theo Ratliff, Tony Massenburg, Kevin Ollie, Kurt Thomas, and Nazr Mohammed, who played for 17 seasons with eight teams.

Associating With Michael Jordan, “His Airness”

Michael Jordan is undoubtedly one of the greatest players to ever play professional basketball, if not the greatest. The only player to ever amass over $1 billion in lifetime earnings and the first former player to be a majority owner of an NBA team, Jordan is a six-time NBA champion, six-time NBA Finals MVP, five-time NBA MVP, 14-time NBA All-Star, 10-time All-NBA First Team member, 10-time NBA scoring champion, two-time inductee to the Basketball Hall of Fame, and two-time Olympic gold medalist.

Jordan, in effect, had four NBA careers. His first, ending with his first retirement from the Chicago Bulls in 1993 following his father’s death, ran for nine seasons, during which Jordan only played for the Bulls. He secured three championships during this career. His second career, starting in 1995 following the Major League Baseball strike, lasted until 1999 – also only playing with the Bulls and also securing three championships.

As minority owner and president of basketball operations for the Washington Wizards, Jordan decided to lace up and play again – this time, for the Wizards – in the name of charity. Injuries and the constraints of age limited him to only two seasons, however. In 2006, Jordan became minority owner of the Charlotte Bobcats. In 2010, the league approved Jordan’s petition to buy a controlling stake of the team, making him majority owner.

While his position as an owner keeps him in contact with players, the node graph did not consider these relationships.

Through his 15 seasons as a player, Jordan can be linked to 110 players. Most of Jordan’s connections are second- or third-order, meaning that there is at least one intermediary between them. This is due to the amount of time since Jordan last played.

Associating With Kobe

Kobe Bryant is undeniably one of the best players currently playing. He is a five-time NBA champion, 17-time NBA All-Star, 11-time All-NBA First Team member, and two-time Olympic gold medalist. Bryant’s recent retirement announcement has caused stirs throughout the league and especially in Los Angeles, where Bryant has been the cornerstone of the Lakers for two decades.

Despite being drafted for the Charlotte Hornets, Bryant played only for the Lakers, making him the current record holder for the longest stint playing on a single team. Over 20 seasons, Bryant has been on the roster with 142 players. Besides his long tenure as a Lakers starter, Bryant’s two terms on the American Olympics men’s basketball team and repeated All-Star appearances helped to make him a well-known face in the league – although the node graph only considered relationships through official NBA play. The majority of Bryant’s connections are first-order, or directly connected to him.

Associating With KG

Kevin Garnett is the marquee player for the Minnesota Timberwolves and the holder of several of the franchise’s records. Despite a chaotic career filled with seasons of being severely unsupported, several turbulent trades, and personal strifes both on and off the basketball floor, Garnett managed to win an NBA championship, be named NBA Most Valuable Player, make the NBA All-Star Team 15 times, and secure the NBA’s rebounding title four times.

In his 21 seasons, Garnett played for the Timberwolves for 13 years, the Boston Celtics – where he won his championship – for six, and the Brooklyn Nets for two years. Over his career, Garnett has collected 200 connections with active players. The majority of Garnett’s connections are first-order connections, or connections directly linked to him.

Associating With King James

There are few players taken seriously as a challenger to Michael Jordan’s throne as the greatest basketball player ever. However, LeBron James – the two-time NBA champion and two-time NBA Finals MVP – regularly enters the conversation as a strong possibility. Relatively young in terms of his professional career, James has experienced more success off and on the floor than Jordan has over the same amount of time. He’s an 11-time NBA All-Star selectee, nine-time All-NBA First Team pick, NBA Rookie of the Year, and AP Male Athlete of the Year, and his four consecutive NBA Finals with the Miami Heat have convinced many that James is the quintessential league player.

James has played for 13 seasons; nine in Cleveland for the Cavaliers and four for the Heat, where he secured his championships. He is connected to 121 current NBA players; however, James’ connections are mostly of the third-order or higher.

Conclusion

The world is a small place. If you take the time to question your connections to others, you could discover that you are linked to virtually everyone and everything in existence. This is especially true in the NBA, where a shared love of the game and competitive camaraderie have linked the players – past, present, and future – into a tight-knit community.

Methodology

Go back to the intro

Using NBA roster data from Basketball-Reference.com, we created a data set containing each player’s name, the team he played for, and the year he played for that team. If he played for multiple years or multiple teams, each pairing counted separately. With 4,336 players on 104 teams, we were left with 23,919 player and team pairs over 70 seasons.

The second data set matched players who played together. This yielded 181,886 player-to-player pairs over 70 seasons. Players who were involved in trades for each other are listed as having played together.

Using Gephi, we built models and set up the entire NBA graph in a timeline to emphasize that players who played together in the 1950s tend to cluster together with one another and not with players who played together in the 1990s.

Colors are the result of clustering at a higher level, where players of one “color group” associate mostly with each other, and not as much with other groups. For example, for Michael Jordan, you can see his time with the Bulls separated into two distinct color groups (yellow and red) where players intersect but played more times with other members of their group. The third group shows his time with the Wizards (green) where most of the group is separated from other players in Jordan’s social network.

We then built a set of shortest paths among currently active players plus everyone they’ve played with. This contains about 1,517 total players. The distance, how many hops to connect any two players, table, and shortest paths list came from applying the Floyd Warshall Algorithm.


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