tapitsbo raises some important points to consider whenever trying to frame this and define the elements properly. Deep politics is everything that's denied or concealed, and often involves the formal state. Example: the rationale for the Iraq invasion of 2003, as opposed to the official narrative which is still taken seriously even by liberal critics who frame it as an adventure undertaken on the basis of a mistake. This is the truth behind the "vanguard of lies" that protects it, in words that Rumsfeld borrowed from Churchill.
Deep state in the U.S. is, roughly, "the industry that hollows out the official state," the combination of the security and power agencies with their contractors and clients, the MIC or National Security state. Deep state elsewhere may have a different form, or even a kind of single core, as is much easier to imagine with smaller countries that have more clearly defined roles in the geopolitics, like Turkey.
The "purely conjectural networks" (many of them not at all conjectural) ensconce themselves within such structures and extend into many others, seeking to effect given missions or just engage in parapolitical plunder. This generally is parapolitical action (what people conventionally call conspiracies and cabals, though I prefer to think of them as operations if they are one-time - generally illegal - or "clubs," which is what they called it in the case of the Safari Club).
Usefully, we can also define the classes to which these structures are accessible and among whom these practices come most often into play as a relatively concentrated power elite that draws from the national security state apparatus, the moneyed "Overworld," the corporate management and relevant sections of the governmental policy apparatus, and the upper reaches of the political classes.
What unites these sectors into a single subject that can be called "deep" is, above all, the element of secrecy. There is a great leveraging and concentration of power that comes from being able to act in secret, to have secret policy and planning, to have freedom from political oversight, to conceal or classify information, to expect open access to others' information, to compartmentalize, to declare knowledge proprietary, to access and development proprietary and secret technological systems, to break law on the basis of a higher justification, to practice deceptions on the public, to determine without an open process what the acceptable risks and costs of collateral damage or even direct sacrifices may be, in many cases even to determine states of exception on the authority of a limited group and in secret, etc. etc. These are powers, once they exist, to which people with the following various qualities of mind (among others) will naturally gravitate: ruthlessness, greed, desire for power and control, self-certainty, absolute faith in a given mission. It's like an invitation to crime. (So is the state itself, libertarians would argue. So is any concentrated organizational power, anarchists would argue.)
And, second, the justifications of national security: self-defense, preemptive self-defense, preventive or eventually assumed self-defense, response to enemy action, assumption that evil and unscrupulous enemies are acting in the same fashion without limits and must be counteracted by any means necessary.
I love a good poo-poo joke. Seriously though, that's a metaphorical slap, right? I hadn't considered you the bitchslap type.