Mutations in the Body Politic

A question: are we connected because we are collective, or are we collective because we are connected? Another, related question: in the "network society," is it possible to reformat the body politic without resorting to the paradigm of modern sovereignty?

The overarching argument made in this essay is that networks, swarms, and multitudes are examples of mutations in the contemporary body politic. These mutations are structurally innovative, but politically ambivalent. In some contexts -- such as that of the various anti-globalization movements -- they contain the potential to become politically radical. In other contexts -- such as that of the diversification of international economic organizations -- they become conservative or reactionary.

The mutations of the body politic -- networks, swarms, and multitudes -- each emphasize certain facets of material politics today: the technological model of networks, the biological model of swarms, and the political model of multitudes. However, when viewed as expressions of a body politic, they also become more than just technological, biological, or political. Networks, swarms, and multitudes are instances in which the very notion of a political body is constantly renegotiated. But the character of this renegotiation harbors an ambivalence within itself. Often, the terms employed are different than, but not necessarily opposed to, those of the tradition of modern sovereignty.

That tradition has been extensively analyzed on a number of fronts. The language of the "social contract" and sovereignty is still with us today, but in a different form. The very notion of a body politic in Hobbes, for instance, posits a strict division between the chaotic, sub-human threat of the "state of nature," and the resulting political order (established by the transfer of rights to the sovereign and the creation of the Commonwealth). This image of the body politic -- hierarchical, compartmentalized, and mechanistic -- is a model significantly influenced by modern anatomical science (in this sense Vesalius' anatomy text De Humani Corporis Fabrica is the scientific corollary to Hobbes' Leviathan).[1] To this model we see variations, such as Grotius' juridical formulation of the covenant, Machiavelli's unruly "plebs," Spinoza's "democratic" multitude, and Rousseau's organicist description of the "general will."

In our current context of Empire, the "network society," the "society of control," and so forth, we know that techno-utopianism has its political limits. That the Internet displays a distributed or decentralized topology is not an indicator of the inherently democratic principles of information technology. In fact, in many cases it has had the reverse effect, by canalizing online activity, stifling innovation, "globalizing" access (e.g., WSIS), and generally preventing the concurrence of critical and technical thinking ("don't think, click"). Caught between the extremes of technical innovation and political conservatism, new technologies seem to promise social and political change at the same time that they categorically disable it.

Thus, the major problematic explored in this essay is whether or not the prevalence of networks, swarms, and multitudes signals a set of viable alternatives to the traditions of modern sovereignty, while still expressing a coherence which can critically and radically weave together technology, politics, and "life itself."

Questioning Connectivity, Querying Collectivity

To begin with, let us take two examples of group phenomena. One example is the various forms of collective dissent and protest which has recently been manifested in a wide range of contexts -- what we can call "distributed dissent." The paradigmatic case study here would be the 1999 Battle for Seattle at the WTO summit, and, in particular, the coordination of protests by the Direct Action Network. The literature on this and other anti-globalization movements is paramount, and will not be summarized here.[2] As part of the anti-globalization movement, the events in Seattle were noteworthy for a number of reasons. One reason was that the form that the protests took was not exclusively based on a mass gathering of bodies at a centralized, highly visible location. Instead, so-called "affinity groups" -- from pro-democracy supporters to anarchists -- organized themselves on a local level, dispersing themselves in and around downtown Seattle, thereby frustrating the containment and control of riot police (and sometimes of the movement itself). Another, related reason the Seattle events are noteworthy was their use of mobile and wireless technologies. As is well documented, the use of mobile phones, pagers, and other technologies was a significant factor in enabling affinity groups to communicate and coordinate their movements within the city. While most interpretations of the Seattle protests strictly deny that anti-globalization movements are technologically determined, what is often noted is this link between distributed dissent and mobile/wireless technologies. Collectivities go by many names, including "smart mobs" and "netwars."[3] Most recently they have cropped up in ad-hoc, participatory performances of "flash mobs."[4] Case studies, such as the People Power II protests in the Philippines, the ongoing Zapatista resistance, and the international F15 demonstrations, all share this combination of collectivity and connectivity.[5]

A second example, of a very different sort of phenomenon is the rapid spread and equally rapid control of Severe Acute Respiratory Syndrome (SARS) that made international headlines in 2003.[6] According to WHO figures, in the span of three months the SARS virus spread from China to Hong Kong, Taiwan, Canada, Singapore, Vietnam, and the U.S., with over 8,500 confirmed cases worldwide.[7] While the SARS epidemic pales in comparison to the still-growing cases of AIDS worldwide, the condensed time-span of SARS was instructive for a number of reasons.[8] As the oft-repeated narrative of SARS makes clear, the success of the virus was significantly boosted by the transportation networks of air travel, resulting in travel restrictions and increased medical surveillance at selected airports. In addition, the rapidity at which WHO and CDC officials were able to control the outbreak was largely the result of informational and communicational networks. The WHO's "Global Outbreak Alert and Response Network" utilized information networks, central servers, and medical informatics, to advise on travel restrictions, treatments, and quarantines. Put simply, the SARS epidemic reminded us, in a highly condensed manner, of the ways in which biology is a network phenomenon; but it also demonstrated the ways in which SARS was much more than a biological network, but was a technological, economic, and political one as well. More specifically, biology is globalization. What began as a basic threat to the biology and health of individuals, also became a biopolitical threat to populations and nations, affecting travel, commerce, and national security.

For a number of years, a growing number of researchers in biology, epidemiology, and molecular genetics have taken note of these network properties of biological life.[9] Currently, a loosely knit group of scientists is building upon this knowledge, exploring the ways that networks inform living, social, and technical systems, as well as the ways in which the life-like properties of emergence and self-organization inhere in networks. This "network science" research has sought to find the common network principles in phenomena as diverse as the Internet, AIDS, and terrorist organizations. What is particularly noteworthy about network science is that it has its roots in biology, since studies of complexity and self-organization often make some sort of tentative claim to "life."[10] For instance, at the species level, research in "swarm intelligence" has shown how ants, bees, wasps, and other "social insects" are able to carry out sophisticated tasks in a self-organized manner.[11] At the level of micro-organisms, researchers have shown how bacteria are able to sense their environment and each other using "quorum sensing."[12] At the molecular level, the study of post-genomic "systems biology" has shifted the gene-centric study of life to the systems-wide level of metabolic and genetic networks.[13] Each of these examples has in common a global pattern that emerges from a set of local interactions, and a whole that cannot be deduced from the analysis of individual parts.

Thus, we have two examples of group phenomena: one political and the other biological. On the surface, there is no relation between them, except at the most general, metaphorical level. Certainly, it would be ludicrous to compare the genetic networks in a cell to the ideological underpinnings of a hundred thousand protesters. Indeed the point here is not to carry out such literal comparisons, either to suggest that politics is self-organized life, or that life is political self-organization. What we can deduce is a better idea of two concepts that inhere in both of these examples: collectivity and connectivity.

We can begin by defining collectivity as an aggregation of individuated units in relation to each other, with the quality of the relations largely specified by the context. Collectivity presupposes spatial organization, though this spatial organization does not necessarily require spatial proximity.[14] The property of "aggregation" in a collectivity is not simply a centralized, spatial clustering; a collectivity can aggregate by dispersal as well. Yet, if a collectivity is not defined by a centralized clustering, then what holds it together?

This is where we see collectivity tied to connectivity. We can define connectivity as a way of relating individuated units within a wide array of possible topological configurations. Connectivity is more a status than a state or a thing. Connectivity is a "status" in both the technical and political sense of the term. Connectivity can be high or low, it can be wide or narrow, and it can be centralized or decentralized. Connectivity is not synonymous with "relation," but presupposes it. Connectivity can happen for no reason at all, but it usually requires a context (or at least a pretext). The most basic connectivity -- a link between two units -- assumes a set of common terms under which relation is possible.

Note that while connectivity may be a prerequisite for collectivity, the reverse does not apply. Connectivity may happen at a widespread level, without any aggregation or group phenomenon manifesting itself. For instance, a large number of people may voice dissent over a political situation, but this does not form a collectivity until those bodies are organized in some manner toward some agreed-upon action. However, a collectivity does require a minimum threshold of connectivity. Indeed, a collectivity is constituted by connectivity. In some cases, a unique use of connectivity enables distributed forms of collectivity to take place.

The distinction between collectivity and connectivity is relevant because it points to a common misconception in many analyses of network phenomena: that connectivity immediately implies collectivity, and that the mere existence of this collectivity points to the emergence of a political form (often, a more direct or unmediated form of democracy). Such intimations are found not only in technophilic accounts of information technologies, but also, somewhat surprisingly, in network science research.[15] The danger of this view is that the conflation of connectivity with collectivity leads to a kind of politics in which simply getting online becomes synonymous with political activism.

I would propose that it is in this tension between collectivity and connectivity that aggregations or group phenomena become political. It is, also, in this tension that group phenomena become "living" as well, with all the social and ideological baggage associated with that term. The claim that is often made is that the examples of distributed dissent are unlike traditional models of protest and activism. Their horizontal, distributed properties make them significantly different from centralized forms of mass protest. Likewise, the biology of complexity, networks, and swarms is significantly different from the kind of biology traditionally taught in university classrooms and labs. The "central dogma" of DNA gives way to a gene expression network or epidemiological network that continually self-regulates at the "edge of chaos."

In this tension between collectivity and connectivity we also find a tension between politics and biology, between group phenomena considered as political phenomena, and as some manifestation of "life itself." How do the political examples of distributed dissent, smart mobs, and netwars challenge, resist, and transform conventional notions of biological "life"? How do the biological examples described by network science challenge, resist, and transform conventional notions of political power? Thus, between the question of life, and the question of power, lies this ambiguous relation between collectivity and connectivity. Can a unique way of rethinking resistance come out of this tension?

Networks Do Not Exist

It would not be difficult to show that the "network" has become the paradigmatic mode of representing global culture.[16] There is a sense in which networks are suddenly appearing everywhere -- not only in new models of consumerism, entertainment, marketing, and communications, but also in more specific, diverse examples, such as terrorist networks, peer-to-peer networks, and the networks of emerging infectious diseases.

Recently, a loose group of researchers in various fields (physics, mathematics, biology, computer science) have been studying networks as a general property of particular phenomena -- that is, as a kind of ontology. Often referred to as "network science," this interdisciplinary research combines concepts from complexity (self-organization, emergence, stymergy) towards the quantitative analysis of a wide range of different networks. Albert-László Barabási's group at Notre Dame, for instance, has been studying the common network properties in linking structures on the Internet, the spread of the AIDS virus, and the communication paths in terrorist networks, while Duncan Watts' group at Columbia University has been exploring networks from a sociological and communicative perspective.[17] Network science not only provides conceptual tools unique to its field of study, but it also purports a practical use of these tools in the analysis, construction, and possible instrumentalization of networks.

What, then, is a network? Most fields which study networks -- be they in computer science, biology, or sociology -- make some reference to a branch of discrete mathematics known as graph theory. Graph theory is a strange kind of geometry, a mathematics of connect-the-dots. A standard graph theory problem is posed by the Prussian-born mathematician Leonhard Euler in the early 18th century. Known as the "Königsberg bridge problem," it runs thus: imagine a small isle bordered on each side by the mainland. There are five bridges that connect the isle to the mainland. Can a person cross each bridge exactly once, without backtracking? Euler began his thought experiment by representing each end of the bridges as a dot, and each bridge itself as a line. Though the problem was simple enough to figure out by trial-and-error, with larger data sets (e.g., trade routes, urban planning) the possible answers grew at an exponential rate. As a scientist of the Enlightenment, Euler must have understood the significance of this kind of mathematics for commerce and colonial expansion (as well as simply getting around town). Euler's first graph theory papers attempted to conceptualize networks by abstracting them into things (dots, or "nodes") and actions (lines, or "edges"), and developing formulae for quantitatively analyzing the ways in which nodes interacted with each other via edges.[18]

If we were to analyze the concept of a network in its mathematical foundations, we would find that it begins with a basic philosophical distinction: that networks are fundamentally spatial phenomena. This is evident in Euler's formulation, and it is echoed in subsequent graph theory research: in the work of Paul Erdós and Alfred Reyni on "random networks," Paul Baran's military research on distributed communications networks, and the sociological work of Stanley Milgram on the famous "six degrees of separation."[19] If one were to create a genealogy of network science and network theory, what we would find is this assumption of space as a starting point, evident in graph theory's geometrical bias itself.

The concept of networks is therefore Eulerian. It begins by understanding networks as a spatial distribution of nodes (things) and edges (actions). This in itself requires the separation between individual entities and the local actions caused by them: actor and act, node and edge. From this conceptual and ontological premise, graph theory concepts aim to describe general properties of different types of networks. For instance, Mark Granovetter's concept of network "clustering" in social networks suggested that the edges or links between people in a social network could be strong or weak.[20] While the strong ties (close friends) have the effect of local clustering in tightly-knit groups, it is the weak ties (acquaintances) that maintain the overall connectivity of the network between clusters. Similarly, Barabási's study of network topologies has suggested that most networks follow a "power law," in which many nodes have few links, and a few nodes have many links (resulting in a decentralized topology).[21]

From the network science perspective, the network is essentially spatial, and the universal properties it displays are not so much evident in the dynamic functioning of the network, as they are static patterns which exist above the temporality of the network. In fact, when we speak of a "topology," we are in effect speaking of networks as spatialized, mappable, discrete entities. The work by Barabási's group shares some general conceptual assumptions with other network science researchers concerning the nature of networks. The first general principle is connectedness: everything is connected, nothing happens in isolation. The second principle is ubiquity: connectedness happens everywhere, and it is a general property of the world. Finally the third principle is universality: networks are universal and their general, abstract properties can explain, describe, and analyze a wide range of phenomena.[22]

If networks are Eulerian in their foundations, what are their politics? This does not mean the ideological struggles of particular case studies (peer-to-peer, virtual sit-ins, the digital divide, etc.). Rather, it is more a question of political ontology -- what is the difference between a "power law" and a power relation? One way of answering this is to return to Euler's historical context of the Enlightenment. Also living in Königsberg, and perhaps crossing the same bridges on daily walks, was Immanuel Kant. Though there exists records of sparse communication between Euler and Kant, it is known that Kant was aware of Euler's work in mathematics.[23] Kant never wrote extensively about networks, but he did write about geometry, particularly as it pertained to cognition and the faculty of reason.

Kant, like most political philosophers, viewed politics as the challenge of managing individuals and groups. But unlike Locke or Rousseau, Kant did not suggest that human beings naturally form groups (and are thus naturally sociable). In what he called the individual's "unsocial sociability," Kant described how social groups arise out of a tension between competition for self-gain, and solidarity for group advantage.[24] We like people, but not that much. We seem to be in constant oscillation between being compelled towards self-sufficiency and recognizing the need for others. Politically this tension is expressed as a tension between freedom and right. Kant's notion of political right is, like his notion of freedom, defined in negative terms: do what you want, unless it infringes upon the right of someone else to do what he or she wants.[25] For Kant, the very function of the state -- or more specifically of "Law" -- was to regulate this delicate balance. It results in a combination of right and external law -- reciprocal freedom combined with external coercion, which led Kant to his vision of a "universal State."[26]

In a short essay called "What is Orientation in Thinking?" we see Kant define networks as both political and mathematical. In this essay Kant discusses the faculty of reason using the tropes of orientation and navigation (as one might navigate a ship exploring uncharted territories).[27] Kant imagines being in a completely dark room, in the condition of blindness in relation to one's surroundings. How do we navigate this space? We start by feeling our way around, receiving impressions from things touched. But this is only a start, for in feeling our way around, the sensibility delivers to the categories of our understanding a set of coordinates -- we understand that there is a table to our left, a chair to our right, etc. We must therefore transform ourselves into a node, a point in space, moving through space along coordinate axes. In short, we orient and navigate by assembling coordinate data into a kind of 3-D, virtual model of a space.

For Kant, between any two nodes there is one "ordinate" or "right" edge.[28] Given Kant's definition of political right and freedom, politics becomes an affair of network management. It is not that the right relation between any two nodes is a straight line, but rather, between the ability of any one node to link to any other, there must also be an external Law that oversees and manages the links of the network. This tension between the local flexibility of the nodes to create edges (relations, connections, links), and the global robustness of an external management system (Kantian "Law") is a tension that is as much political as it is mathematical or technical. In this sense the current WSIS meetings are attempts to establish a Eulerian-Kantian model of network governmentality. The Kantian natural law of "unsocial sociability" and the artificial, human-made law of "right" (negative freedom) constitute the universal laws or principles which govern networks as political ontologies. The topology of politics is, therefore, a legislative, juridical process between external law and emergent order.

Both Kant (in politics) and Euler (in mathematics) show how an adequate understanding of networks must not come from experience, but from an abstracting, spatializing procedure. Only in this manner is it possible to gain the bird's eye (or God's eye) view of the network, to see the network topology, and therefore understand the best way to manage a network.

But we also need to note a central problematic to this Eulerian-Kantian concept of a network: the problematic of time. While graph theory and topology "map" a network as a set of nodes and edges (individual entities and relations between them), this approach betrays a bias towards a spatialized view of networks. A topology or map of a network is not a real-time representation; it has flattened time into space, showing us all possible nodes and edges. However, even at the level of our everyday experience -- in communication, transportation, and sociality -- networks create affects that are indelibly time-based, dynamic, and temporal. Networks are always living networks: networks that are functioning, and networks that are in process. This means that networks are inherently dynamic, undergoing constant and variable changes, both within the composition of individual nodes, and in the relations between nodes.

If Eulerian graph theory is spatialized, the same also follows for Kant's political metaphysics. Though Kant grants both space and time an a priori status, the way in which they are conceptualized is invariably spatial. Kant spatializes time by configuring it as a container (much in the same way that Newton had).[29] In his analysis of time as part of the sensibility, Kant describes time as a space, as an environment in which things happen: "Time is a necessary representation that underlies all intuitions...The infinitude of time signifies nothing more than that every determinate magnitude of time is possible only through limitations of one single time that underlies it."[30] Temporality therefore presupposes spatiality: "Time has only one dimension."[31]

The problematic aspects of this view are seen in Kant's discussion of "motion and alteration." Kant's analysis of time does not accept motion and alteration as constituent elements of time. For Kant, to be able to conceive of motion or alteration is to presuppose an environment (time) in which and through which change and alteration can occur: "Motion presupposes the perception of something movable...Time itself does not alter, but only something which is in time."[32] Thus temporal, ephemeral processes such as motion and alteration are a posteriori, dependent upon our prior framework of space and time. Change can only be accounted for through a prior concept of time (but a spatialized, "container" time).

If we consider Eulerian and Kantian concepts of networks, it appears that dynamic change -- the very thing that makes a network a network -- is only a by-product.[33] This view of networks can only accommodate dynamic change to the extent that it can spatialize that dynamic change, or to the extent that it can spatialize time.

One of the most consistent critiques of this Kantian notion of time is the one carried out by Henri Bergson. For Bergson, exactly the opposite is true: the process of change is constitutive, and our concepts of space and time derivative, a posteriori tools which we use out of convenience and practical necessity.[34] Bergson's concept of "duration" is meant to diversify our understanding of time, and by extension our understanding of the process of change. In Bergson's early work, the notion of duration conceives of time in two parts: as an external, quantitative, discrete time, and as an internal, qualitative, continuous time.[35] While this is often interpreted in psychological terms ("clock-time" vs. "inner time"), Bergson's later work goes on to complicate this notion. In his studies on memory, cognition, evolution, and relativity, Bergson repeatedly attempts to show how duration is not just an effect of subjectivity, but that duration is an ontological reality.[36] Bergson's notion of duration reconfigures time as persistent and resistant -- qualitative (not quantitative), continuous (not discrete), and intensive (as opposed to extensive, or spatialized).

Bergson's sporadic comments on Kant can be summed up in a number of short comparisons, which provide us with an alternative to the Eulerian-Kantian view of networks.[37] Contra Kant, Bergson does not accept that sensibility (space and time) is an a priori faculty. Rather, Bergson sees time and space as a practical means of understanding the world in static, spatialized terms. "Time" in this sense is spatialized time, and qualitatively different from the notion of a flow of time, or more importantly, a time that is identical with change.[38] Bergson's concepts of "creative evolution" in biology, and the "open society" in sociology, are examples of this concept of time-as-duration carried out in practice. Biological morphogenesis and evolution, as well as societal transformation, can only be understood, says Bergson, in the context of time, and as time itself. Time, for Bergson, is not a Kantian-Newtonian container, but is constitutive; things do not happen in time, but are rather constituted as duration.[39]

We are thus left with a conundrum. On the one hand there is the concept of a network, which, as we've seen, has its technical roots in the field of Eulerian graph theory, and its political-philosophical roots in Kant's metaphysics. On the other hand, we acknowledge that any definition of a network must take into account the constitutive, dynamic aspects of networks as being rooted in temporality. Both views present us with a concept of networks that is spatialized, static, and universal, even when considering time and change. Bergson's critique of Kant, and his concept of duration, point to the ways in which we habitually understand time in terms of space. On one hand, a network is that which maps a static pattern above and beyond the particular, ephemeral state of the network; on the other hand, a network is that which is defined by dynamic change.

This tension boils down to the distinction between network effect and network affect. When we want to understand either the effect of a network or the modification of a network (be it the Internet, SARS, or terrorist groups), we require concepts which both totalize the network as a whole, and break down that whole into constituent parts (nodes), from which relations (edges) can then be derived. The pattern that results -- the topology -- is an index of the fundamental character of that network's measurable effects.

By contrast, understanding network affect -- the ethics of sharing information, the globalized context of infectious disease, the political conditions of fundamentalism -- requires more than quantitative analysis or the search for static patterns. This is because, in a network, affect is disengaged from emotion. This point cannot be overstated: in networks, affect is not emotion. Affects are "affections of the body by which the body's power of acting is increased or diminished, aided or restrained, and at the same time, the ideas of these affections."[40] Affect is networked, becomes distributed, and is detached from its anthropomorphic locus in the individual. In a dynamic network, the individual does not possess an emotion, but is rather constituted through the circulation of affects. The affects may circulate at many levels (biological, social, economic) and via more than one type of network. But the network affect is the living, immanent topology of the network, not the abstracted, transcendent pattern above the network.

This discussion of network affect will lead us, in the next section, into a discussion of "swarms." For the moment, we can say that, in a sense, networks do not exist. They do not exist precisely because their dynamic existence cannot be fully accounted for within the tradition of the Eulerian-Kantian network paradigm. From this perspective, networks can only be thought of within a framework that spatializes time, and yet this excludes precisely what is constitutive to most networks -- their dynamic properties.[41]

Living Networks

Once we take into account the aspect of time-as-duration in networks, then the question is how networks themselves change. It would seem that in considering networks as existing in time -- as living networks, as network affect -- the separation between nodes and edges becomes more complicated. Could we say that, when we consider networks as living networks, we arrive at a situation in which nodes equal edges, in which nodes are edges (things are tasks, actors are acts)?

Before more fully exploring the implications of such a view, it would be worthwhile to reconsider our view of networks thus far. As we've seen, much thinking about networks is based on a mathematical (Eulerian) and political-philosophical (Kantian) paradigm, in which the inherently dynamic qualities of networks are spatialized, and abstracted into a static pattern called a topology. While this view of networks privileges the relations between things, rather than things-in-themselves (edges rather than nodes), it also cannot account for the dynamics within networks; dynamics that show us a more complicated view of the separation between nodes and edges.

While the Eulerian-Kantian paradigm of network thinking is very useful for certain problems (routing traffic on a computer network, for instance), we have also seen that there are a range of other contexts that are much more than the spatialized, static networks portrayed in graph theory and network thinking. The examples cited earlier -- distributed dissent, the self-organization of insects, patterns of infectious disease -- are certainly networks, in that we can readily identify a set of nodes, and a set of relations between nodes, or edges. But they are also much more than networks, for there are changes which take place within individual nodes (changes in political ideology, changes in environment, mutations in a virus), and between individual nodes, resulting in edges or relationships that create or change nodes (joining a cause, emergence of tasks, modes of transmission). Above all, nodes are never fixed; they are in constant movement -- movement of people, movement of species, movement of molecules.

What would it mean, then, to think of networks as living networks, as networks ontologically driven by time and by duration? A number of modifications to the Eulerian-Kantian network paradigm would follow. For instance, networks are not flat or uni-dimensional, but can overlap and co-exist; that is, networks can be layered, giving us topological layering. A biological network, such as an infectious disease, is not just biological, but, in our contemporary, globalized context, it also participates in transportation networks (air travel) and communication networks (WHO website updates). Another modification that follows is that not all nodes are equal, just as not all edges are equal. Networks can also display a topological diversification. An infectious disease is not the same at every locale, but may display different rates of transmission and mutation in a food-processing factory, in an airplane, and in a densely packed urban environment. This would therefore call for different modes of perturbing this network. Furthermore, networks need not have a single topology, a single identifying pattern -- a network is really a set of multigraphs and polygraphs understood to exist in time. An infectious disease network may start out as a centralized pattern, radiating from a particular city or environment, but then, due to its layering and diversification, it may change into a more decentralized network. Finally, and most importantly, a network existing in time is not just extensive, or a map of fixed nodes (or things) and stable edges (or relations); a living network is also intensive. Networks can intensify or de-intensify, depending on the quality, force, resiliency, and flexibility of the relations. Topology is not an extensive mapping, but is instead a topological intensification, culminating in a network affect.

All of these modifications result from understanding networks as fundamentally time-based sets of relations. As mentioned previously, they complicate the easy division between nodes and edges, in some cases resulting in a view of a network as "edges-without-nodes," or a network in which nodes themselves are particular kinds of edges.

Thanks are due to Harry and Dot Bowers for providing an environment for research and writing. Thanks are also due to CTheory for their editorial assistance.