http://en.wikipedia.org/wiki/Graph_%28mathematics%29
&
http://en.wikipedia.org/wiki/Topology

Let us discuss the current configuration and results of the island teleport network (abstractly understood as a connection or 'edge' on a graph).

Essentially my point is that gamma, and beta, are isolated to alpha-bridges.  This makes player corps have to assault through alpha to beta, beta to gamma.  At some point, once the two pairs of beta and gamma are locked down, it basically becomes an overwhelming task to actually assault and occupy any island from that point. 
Sparsely connected graphs create their own isolated subgraphs, or nodes, that then become easy bottlenecks to defend; this results in little turn-over as it is easy to defend such a bottleneck.  I think you see this in other games like EVE, where alliances frequently pit valuable PVE/Indy functions in deeply buried systems with little connectivity.

The cost of moving from one island to the next is the sum of the edges (and weights) they must teleport over.  Alpha is easy to move about freely, due to non-pvp status, but is costly in time/logistics.  Beta may cost more or less depending on if it is occupied and by whom.  Naturally an opposing faction would increase overall 'cost' of trying to move through this way. 
Beta and gamma are currently sparsely connected as a whole, being isolated to 3 well-connected subgraphs that form their own cycle, which has several tendencies that can be observed since the gamma re-release. 
Once a Player-alliance controls a beta, it becomes significantly easier for them to control the other 3 beta and gamma in this subgraph.  Generally, if all things being equal, the first to establish a foothold will go on to conquer the rest. 
This is the first 'state', after which for other factions to successfully take over and maintain control over ANY of these islands in this connected group of 4, they would generally have to route out the rest of the opposing faction, otherwise the opposing faction has the same logistical power and tactical advantage of being already well established, able to be reinforce from the other islands that are under control.  [Note: this assumes diplomacy and general niceness/sharing, etc is not part of this thought experiment]
Logically, the opposing factions would want to control the entire subgraph for this bottleneck advantage, betas becoming a strong front-line that can protect perhaps more valuable investments on gammas.

What I argue is, without additional gamma-gamma connectivity, beta-gamma control by player factions will be increasingly static due to the overwhelming advantage of controlling access by this 'bottleneck' of beta.  Also, gamma bases have substantially better defense mechanics over beta outposts, increasing the cost of assaulting such a base, and therefore island.  If one wants to assault any pair of gammas, they must first establish and control a beta-logistical pipeline well enough to establish themselves on a gamma, from which they could stage an assault. 

Gamma would benefit from becoming interconnected, perhaps as its own larger cycle. 
Naturally this is all assuming these opposing factions are all relative in size and activity.  I do not speak about current population or involvement, because if we design factors around this, those assumptions would quickly give way as population shifts occur.  Also there goes the incentive to lock down more islands, as it wont isolate any bottlenecks, each island is just as vulnerable based on the state and quantity of its neighbors.

PS:
A similar analysis should be performed with regards to spark teleporting.  As it negates the path-cost for established player factions, which leads to the ability to strongly defend multiple entry points, with the same numbers of equally matched enemies.  Power, if more localized, would result in more opposing factions per class of island, as the ability of any single one, to control many would be limited, and they would be better suited maintaining current boundaries from incursions and avoid spreading thin.

TL;DR
Gamma->Gamma TP connections and/or more gammas would result in more PVP, and more different factions being involved in PVP: cause math n' stuff.
Spark Teleporting should be revisited: see multiple other threads about that. [IE: increase cost/introduce more limits/remove]