Network Typology

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Characteristics of Networks

Networks and Complexity

Dave Snowden at

1. If it's a network, you can draw it.

2. Every network has an underlying purpose and every network creates value.

3. We can create a language of networks that enables us to identify, create, and alter its properties, boundaries, and environment.

4. We can approach working with networks by understanding them as complex systems.

5. Everyone in a network can influence the relationships in it and its outcomes.

6. Norms, especially reciprocity and trust, are required for networks to be successful.

7. Success networks are generative and reflective.

8. All networks are alike (have the same fundmental discernible properties) and all networks are unique (in how they express those properties) (

Types of Network

By Relational Logic

Mark Cooper:

"Reed identifies three types of networks that create value.

First, there are one-way broadcast networks. Also known as the Sarnoff “push” network, the value of one-way broadcast networks is equal to the number of receivers that a single transmitter can reach. An example of a one-way broadcast network is the wire service.

Second, there are Metcalfe networks. In a Metcalfe network, the center acts as an intermediary, linking nodes. Classified advertising is an example of the Metcalfe network.

Third, there are Group Forming Networks, also known as Reed Communities. In this network, collateral communications can take place. The nodes can communicate with one another simultaneously. Chat groups are the classic example of this type of network.

The key difference between the Metcalfe network and the Group Forming Network is multi-way communications. Group Forming Networks use group tools and technologies such as chat rooms and buddy-lists that “allow small or large groups of network users to coalesce and to organize their communications around a common interest, issue, or goal.” The exponentiation increases value very quickly and may cause the number of connections/communications to exceed the ability of individuals to maintain them. Thus, it is a theoretical upper limit. On the other hand, as Reed points out, the formation of even a small subset of the theoretically possible groups would dramatically increase the value of the network - N3 in Exhibit 3. Even if not all groups form, the potential value in the option to form groups is higher. The critical point is that to capture the value of group forming networks, the members of the network must have the freedom to self-organize groups. With that freedom, they create the groups of greatest value to the users. " (

See also:

  1. Metcalfe's Law
  2. Reed's Law

By Structure

Most definitions and excerpts are by Andrew P. Smith at

Ordered Networks

The simplest types of network are those in which each node has a relatively small and fixed number of links to other nodes. I refer to such networks as ordered. A good example is provided by a crystal, such as diamond, composed of carbon atoms, or quartz, composed of silicon atoms. Each node, or atom, has links, or chemical bonds, with several neighboring atoms, and only those atoms; this results in a highly regular lattice structure. Any one small portion of such a network looks exactly like any other portion.

Random Networks

A second general class of networks is represented by those whose nodal members are connected randomly. Rather than having a fixed number of links per node, this number can vary somewhat. If the number is truly random, however, then there is a well-defined average number of links per node, as well as an equally well-defined coefficient of variation of this average. So if we were to plot the number of links per node against the number of nodes, we would get a Gaussian or Poisson distribution--a symmetrical peak tailing off on either side (Fig. 3B). Most of the nodes in the network have about the same number of links. Relatively few nodes have many fewer links than the average, or many more links.

Scale-Free Networks

The most interesting kind of networks, and those which have received the most attention and publicity recently, are known as scale-free. In this type of network, there is an inverse relationship between the number of links per node, and the number of nodes with this many links. That is, most nodes have very few links, and the more links a node has, the more uncommon it is. So when one plots the number of links per node against the number of nodes, one gets an exponential curve (Fig. 4B), or a straight line on a logarithmic scale. This kind of relationship is also called a Power Law distribution, and is a characteristic feature of scale-free networks.

Assortative vs. Disassortative

  1. Assortative Network
  2. Disassortative Network

"In assortative networks, well-connected nodes tend to join to other well-connected nodes, as in many social networks — here illustrated by friendship links in a school in the United States.In disassortative networks, by contrast, well-connected nodes join to a much larger number of less-well-connected nodes. This is typical of biological networks;" (

By the strength of social ties

Ross Mayfield [1]:

(1) Political Network

"In a representative democracy, people are elected to carry the burden of political activities and decisions. Our vote is our proxy of affinity. A vote is not a strong tie and there is no personal relationship between the candidate and citizen. The elected optimizes their activities to serve and appeal to a constituency. Lots of babies get kissed, but few remembered aside from a generalized picture of how their future should be decided.

So too in mass media. A subscription is a vote and the media outlet serves an audience similar to a constituency. Weak ties between the media hub and subscribing node allow the hub to scale. So does the set of activities the hub engages in, by limiting the time committment to each subscriber through a more generalized service. Hubs respond to changes in their subscription base, constantly polling trackbacked referrer log opinion, reframing their content to appeal to the ever-growing base.

The Political Network is based upon representative weak ties instantiated by a link. A hub designs itself as an institution, optimizing the transaction costs of information flow for point-to-multipoint distribution and feedback. This allows it to scale -- creating a Scale-Free Network, or Power-law distribution.

But within the Political Network each hub also has its own Social Network. This Social Network of stronger ties has a lower transaction cost of passing information, and consequently, sways the activities and decisions of the hub with greater influence than the readership.

(2) Social Network

The Social Network is based upon functional weak ties instantiated by an investment in time such as conversational inter-linked posts. An Social Nework is transactional by nature, with the means of establishing a relationship commoditized. Close to the Law of 150 in scale, a time investment is made each node to be at least peripherally concious of the other nodes and the information flow between them.

One design challenge for social software is extending the capabilities of people to hold a higher number of meaningful conversations and cultivate relationships. This is what Clay calls Blogging Classic, on steriods. The capability to extend the time and space of relationships.

Similar to the network distribution of Photography e-commerce sites category in the NEC Paper, it deviates from the Power-law.

(3) Creative Network

The Creative Network is based upon functional strong ties with an active and continious time investment. Instantiated by real world relationships with a firm foundation of trust with dense inter-linking. This is the core of a person's network, serves as the basis for regular collaboration and production, leveraging the Strength of 12. This Creative Network is an internal network, that feeds off of the external network (Social Network) for new ideas but is optimized to produce.

The requirements for a relationship of dense of interconnections are so high that what remains is a bell curve in distribution." (

By Commonality

Bruce Nussbaum [2]:

"Communities are bound by emotion and passion. Networks are simply communication linkd among people with something in common. Communities are a special kind of network (perhaps the most important in terms of branding). I'd argue that communities are passionate and emotional."

From Chloe Stromberg:

Emotive networks (e.g., CarePages, -- Commonality: a powerful emotional experience, like being diagnosed with an illness or loving a particular type of car. Motivation to connect: find people to share your experience with.

Advice networks (e.g., Berkeley Parents Network, -- Commonality: you're trying to do an activity like parenting in the Bay Area, learning about emerging technologies. Motivation to connect: get suggestions from someone whose perspective you value.

Dating networks (e.g.,, Yahoo! Personals) -- Commonality: you're single, maybe you share similar social values. Motivation to connect: meet a sweetheart (not a community).

Blog networks (e.g., Micropersuasion, Greg Mankiw's Blog) -- Commonality: the ideas that you're interested in. Motivation to connect: affect the public dialogue about the ideas.

Wiki networks (e.g., Wikipedia, CarGurus) -- Commonality: you want the unvarnished, comprehensive truth to be free and available. Motivation to connect: get the whole picture." (

Details on Scale-Free Networks


Examples of Scale-Free Networks

"Scale-free networks have now been shown to exist very widely in both the natural world and in human societies. In the cell, examples include metabolic networks, in which each kind of molecule is linked to other molecules by enzymatic reactions (Jeong et al. 2000); and protein networks, in which protein molecules are linked to each other by physical interactions (Jeong et al. 2001; Wuchty 2001)). It seems likely that some kinds of tissues, particularly the nervous system, also exhibit scale-free organization, though so far the complexity of these tissues has not made it possible to test this hypothesis.6

In human societies, scale-free networks include many kinds of social relationships between people, including networks of acquaintances, business contacts, and sexual partners (Barabasi 2002). It even turns out that if one "links" movie actors who have appeared in at least one film together, one also gets a scale-free network! Other examples include the scientific literature, in which individual articles or papers are the nodes, linked to each other by citations (Bilke and Petersen 2001); and human language itself, in which words are nodes, linked by relationships such as similar meanings or associations in speech and text (Ferrer et al. 2001). Scale-free organization has also been reported for electrical power grids. where power sources are linked by lines to various consumer areas, and airline routes, which link cities to other cities.

The best known and most intensively studied scale-free networks, however, are the internet--the physical structure of servers and individual computers linked by phone lines all over the globe--and the world wide web, the documents or pages of information accessible through the internet. Because of the enormous number of nodes and links involved, particularly in the world wide web, and because this information can be accessed in a straightforward and systematic manner, a seemingly unending amount of data on the internet's organization has accumulated, and has been subjected to rigorous statistical analysis. Much of what is known about scale-free organization has come from this work.

Characteristics of Scale-Free Networks

What are some of the distinguishing features of scale-free networks? As I pointed out earlier, this class of networks is characterized by a few relatively highly linked or well-connected nodes, and a great many others with few links. One important implication of this organization is that such networks are highly resistant to random perturbations. Elimination of a few randomly chosen nodes will usually have little effect on the overall structure and function of the network, because the probability is that these nodes will have few links, and not be critical to the overall organization. This aspect of scale-free networks is thought to account for the fact that the internet and the world wide web as a whole have proven quite resistant to random breakdowns. That is, when individual servers go down, the problem is generally confined to a small region of the web or the internet. The same property may contribute to the resistance of cells to chemical or biological insults, or to mutations; a loss or deficiency of one type of molecule in the metabolic network is unlikely to have serious repercussions for the rest of the network.

On the other hand, scale-free organization turns out to be much more vulnerable than a random or ordered network to a selected perturbation. If one or more of the highly connected nodes--commonly called a hub--is eliminated or compromised, this will have potentially enormous repercussions on the entire network, because so many other nodes depend on these hubs for their connection to everyone else. Alberto-Laslo Barabasi, one of the leading investigators of scale-free networks, has suggested that the Asian financial crisis in 1997, which was triggered by a relatively common failure of a bank to meet certain debts, might have reflected weakening of a critical hub in the financial network. The same principle underlies the potential vulnerability of sources of information, energy or wealth in America to a terrorist attack. And again, if we consider scale-free networks within cells, a biological agent--such as a virus or bacterium--that is adapted to disrupting a key node within the network may have a lethal effect on the cell.

Another signal feature of scale-free networks is that they have relatively small diameters, that is, average distances between nodes. This discovery was actually presaged three decades ago, long before the appreciation of scale-free properties, by the psychologist Stanley Milgram. Milgram claimed that virtually every person in America was no more than six links removed from every other person (Milgram 1967). That is to say, if we select any person at random, he or she knows people who know other people who know others, and so on, who will lead, in no more than six steps, to any other person. This has become famous as "six degrees of separation". While the number may not be as small as six, it is a very small number, and is now believed to apply not just to people in America, but to everyone on the planet.

With more than six billion people on earth, many of them living in areas remote from the rest of civilization, this claim may seem preposterous. The key, however, is again found in the well-connected nodes or hubs. Most people are fairly closely linked to one of these hubs; that is, they know a very well-connected person, or know someone who does, or know someone who knows someone who does. One of this well-connected individual's acquaintances, in turn, will know someone who knows someone who knows...and quickly to any other person. In other words, the few highly linked nodes, well-connected individuals, act as bridges that facilitate contacts between less connected individuals. Because of this property, scale-free networks are also often referred to as small world networks. No node in such a network is very far removed from any other node.

Conditions for Scale-Free Networks

Studies by Barabasi and his colleagues have found that two key factors or conditions are required in a group of interacting nodes in order for them to form a scale-free network (Barabasi and Reka 1999). First, the group must be growing, constantly adding new members. This of course is an obvious feature of human societies, as well as of most artifacts produced by these societies. One could not have a better example than the internet. This property is also a feature of molecular networks within cells, if we take an evolutionary perspective, and recognize that such networks did not emerge full-blown, but rather were created through a gradual accumulation of new molecular partners. The earliest such networks, perhaps found in enclosed structures that resembled cells in some respects, probably contained a relatively few such substances. Over time, the number increased, as new enzymatic reactions made it possible for new metabolites to be increased. As Stuart Kauffman (1993) has shown, as the number of substances increases, so does the probability that one substance will be capable of catalyzing the formation of another substance. Once this occurs, links between substances can be formed.

A second critical feature of scale-free organization is that new nodes must preferentially link up to other nodes that already have a high number of links; that is, the more links a node has, the higher the probability that it will get still more. This phenomenon is often referred to as "the rich get richer", and indeed, the distribution of wealth in America and most other societies also follows a scale-free organization (Buchanan 2001). That is, rather than there being a Gaussian distribution of wealth, with most people clustered about a mean, there is an inverse or Power Law relationship between any degree of wealth and the number of people who have attained it." (

For updates see Scale-Free Networks

More Information

  1. Network Theory
  2. Small-World Network
  3. Network Topology

Overview entry: Network