Today the computer’s primary role in our day-to-day lives is to find the connections and patterns of value in relations between networked objects, people and places – and sidestep the less valuable ones. This is ‘the graph’, the gargantuan pool of interlinked data that drives Facebook and pretty much all our data-driven world. On Facebook’s network graph that’s 1.65 billion people linked in 280 billion ways. The Open Data Cloud’s 265 linked datasets contain about 31 billion connected facts. Yet size notwithstanding, all networks are essentially the same. ‘Nodes’ – entities or facts, or ‘actors’, usually, but not always, actual humans – linked by lines of connection called ‘edges’ in potentially limitless ways. Newly-minted University of London Professor Peter Wood made the theory of graphs the subject of his inaugural lecture at London’s Birkbeck College this  month, starting with a map of eighteenth century Königsberg (right), with its four quarters connected by seven bridges over the River Pregel. Swiss mathematician Leonhard Euler wondered if you could walk  across all seven bridges without crossing any bridge twice and return to your starting point. Euler’s attempt at a solution consisted of representing the problem by a ‘graph’ with the four city quarters represented by four ‘nodes’ and the seven bridges by seven ‘edges’ (left), and in the process inventing graph theory. Graph theory is a mathematical approach to help model routes through the infinite connective choices provided by our networked world. It allows the transcription of these connective options into algebraic calculations – algorithms. As the algorithms get better at finding shorter routes to the data they need, they are more quickly run through to a result on computers, which are themselves doubling in speed every 18 months, a rule known to many as  ‘Moore’s Law‘. Harvard professor Gary King’s colleague was quoted $2m for a computer big and fast enough to handle the vast data sets he worked with. King and a student wrote short cuts into the algorithm so it could handle the same data, on a laptop, in 20 minutes. “As terrific as the developments summarised by Moore’s Law,” writes King, “they don’t come close to modern data science.” In their book The Exploit: A Theory of Networks, Alexander Galloway & Eugene Thacker highlight Gilles Deleuze’s definition of control of such fantastically fast, vast network: “Not simply manipulation, but rather modulation.” Protocols, system modulators directed by actors, both human and non-human, route information around the network and hold it in place in space and time. The protocols’ capacity to modulate – to modify the organisation of nodes and edges and connectivity – shapes “different topologies of organisation and control” across networks, and how actors within them interact. Networks are distinguished by their primary topologies, but they may also accommodate coexistent alternative topologies at any one time, even incompatible ones. It is why the internet can be simultaneously liberating and repressive, anarchic and rigidly controlled. That’s the whole point of networking, the amalgamation of “antagonistic clusterings, divergent sub-topologies (and) rogue nodes”. It’s what makes them networks, write Galloway & Thacker. If all a network’s nodes were all equally compatible, they would be a single whole and not a network at all. This capacity for multi-layered topologies is not solely due to the way network protocols are modulated. Alternative network maps connect nodes by applying protocols with their own logic of organisation and control. They are enabled by the “exploit” – disruption from within, infiltrated lines of code that disable or subvert the function of existing protocols. Exploits tend to the technically destructive, like the DDoS attacks propagated by both opponents and supporters of Wikileaks, but the exploits that have the most lasting effect are those that supplant old topologies with new ones. The nodes, the data, remains the same, but connected differently under the terms of different protocols. The aim is to create an alternative topology, one with radically different function and identity that disables or subverts the originals. The current example is the exploit that broke the Panama Papers, recasting a secretive finance network into something quite different. Networks are strongly resilient to the experience of reconnection and remapping by new edges and topologies. In fact a diversity of topologies makes a network more functional, not less. At the very least it facilitates transparency, and allow different interpretations of power relations’ interdependency, as was the case with the Panama Papers. If “it takes networks to fight networks,” as David Ronfeldt & John Arquilla have argued, then, counter Galloway & Thacker, it also takes networks to understand networks. “A whole new topology of resistance must be invented, that is as asymmetrical in relationship to networks as the network was in relation to power centres.” A new physics of organisation, they propose, “that is as real as pyramidal hierarchy, corporate bureaucracy, representative democracy, sovereign fiat, or any other principle of social and political control.” It could be, they say, the first step in realising an ethics and a politics of networks, a political consciousness capable of identifying and critiquing protocol modulation, while fostering its transformative capacity. In the meantime today’s network topologies of resistance are defined not only by their edges, but also by their nodes’ identity as unique actors with their own power to modulate. Contesting networks are Real Life tribes at virtual war. Their codes of conduct, or law, or terms and conditions, are applied as exploits, infiltrated lines designed to disable, subvert or destroy topologies of organisation and control. Tribes of lawyers with lines of legalese disabling tribes of Napster users, trolls subverting the bourgeois tribes of MumsNet, Bahraini secret police destroying dissident networks with fake encrypted messages routing opponents into traps. But even if disruption were not so central to the purpose, it would still be pointless to try to preserve the political coherence of a topology of resistance. Combative networks are inevitably reshaped by the simple act of connection with a rival network node. The exploit, no matter how anonymously or covertly applied, simply re-binds a new set of antagonistic clusterings, divergent sub-topologies and rogue nodes – and recasts them as whole new network topologies in which protocols are tuned for competition as well as connection. In his own book A Thousand Plateaus, Deleuze and his co-author Félix Guattari use the metaphor of the “orchid and the wasp,” referencing the biological concept of mutualism, in which two different species interact to form a ‘multiplicity’, a unity that is in itself a multiple. Galloway & Thacker’s topologies of organisation and control are able to co-exist above, below and alongside different, even incompatible versions of each other. These are not multiple topologies of resistance, but a multiplicity of topologies of contestation. An interesting space for a journalist to work.