Discussion I
To start our discussion, let’s to reflect on our current understandings of a network as a concept. In small groups, take a moment to discuss the following questions.
What is a network?
How would you describe a network in simple terms?
In our view, a network is a representation of a set(s) of relationships between one or more entities. The entities of interest to the SENG are usually social or ecological beings. But in theory, any entity can have connections and thus be represented within a network graph.
Networks are frequently used to represent the structure of a social or ecological system. As network scientist Albert-Lazlo Barabasi concluded in his book Linked, “networks are the prerequisite for describing any complex system, indicating that complexity theory must inevitably stand on the shoulders of network theory.” Networks make the intractable tractable. Importantly, networks are purely an abstraction, but they are a useful for studying systems.
Nodes and Edges
But how do we actually represent such complexity?
In network science, we use nodes and edges from graph theory. A node is any entity that is connected to other entities. Nodes often represent the conventional subjects of social and ecological sciences: persons, groups, organisms, populations, organizations, places.
An edge is a the relationship between two nodes. We don’t need edges if our goal is to summarize the attributes of nodes. We can use conventional statistics for that. If we want to understand how individuals are connected and the implications of different kinds of connections, we need edges.
Figure 1: Two nodes (red) connected by a single undirected edge.
Discussion II
Now that we understand the inherent relationality of networks and the way they are represented, let’s think about some examples of networks and how they would be assembled.
What are some examples of networks that interest you?
Who/what are the nodes?
What kinds of edges link the nodes?
Network Forms
Many of the examples that arise is disucssion are associated with several types of commonly used networks. Some of these are relatively simple and others that are very complex. As we move from simple to complex examples, think about different classes of nodes and edges forming specific layers. Simple networks might have just one layer, while more intricate forms may have multiple interacting layers at different scales.
One-mode network.
A network with a single layer contains one kind of node and one kind of edge. These are sometimes referred to as one-mode networks.
Figure 2: A single layer (one-mode) network with 10 nodes.
Many conventional social relationships can be represented with a single layer undirected network. Here are some examples:
- Kinship
- Friendship
- Joint attendance
- Affiliation
- Communcation
- Coauthorship
- Collaborative partnerships
Directed Network
While an undirected network may suffice for many social relationships, there may be reasons you want think about directionality. Take friendship, for example. Although friendship seems like an undirected attribute of a relationship, it is possible that one person calls someone there friend, but that someone does not reciprocate the sentiment. Thus, an advantage of using directed networks is the ability to ask how important reciprocity is to network structure.
In a directed network, a dyad can have one of three edge states (Figure 3):
- 0 = no edge (j, k)
- 1 = an edge in one direction (i, k)
- 2 = reciprocal edge (i, j, and j, i)
Figure 3: A directed triad. Arrows indicate the flow of edges. A reciprocal edge is colored black.
Weighted (valued) Network
A common representation of edges is binary; edges are either present (1) or absent (0). But many edges occur with different magnitudes, so we can envision edges with weights or values. In these weighted networks, edges could have meaningful frequencies or probabilities.
Figure 4: An undirected weighted network. Edges is this network have values ranging from 0 to 3.
Bipartite (two-mode) Network
While a one-mode network only has one class of node with edges that occur within that class, a bipartite networks has two classes of nodes with edges that only occur between classes.
Figure 5: Two-mode (bipartite) network. Note that edges only occur between red nodes (first layer) and blue nodes (second layer).
Because of the strict definition of edges only occuring between layers, bipartitate networks are used for specific kinds of interactions:
- plant-pollinator connections
- host-parasite connections
- individuals attending events
- party affiliations
- policy writing
- place-based connections
Multilevel Network
If a bipartite network has edges that only occur between modes (i.e. interlayer edges), then a multilevel networks has both interlayer and intralayer edges.
Figure 6: Multilevel network constructed using igraph and graphlayouts packages in R. Orange nodes and edges are one layer; black nodes and edges are a second layers; and purple edges indicate interlayer connections.
Suggested Readings
There are many references available to learn about the foundations of the network perspective. This meeting draws inspiration from The SAGE Handbook of Social Network Analysis (Scott and Carrington 2011) and the structures outlined by Bodin and Crona (2009). Our discussion of SENs draws on the ideas expressed by Sayles et al. (2019) and the well known article on Disentangling Social Ecological Systems (Bodin and Tengö 2012).
Social Ecological Network (SEN)
SENs are a specific kind of multilevel network in which one layer contains social interactions (e.g. cooperation, sharing, communication) and another layer contains ecological interactions (e.g. migration, dispersal). These layers are connected with interlayer edges that specify how the social process is linked to the ecology and vice versa.
Figure 7: A social-ecological motif following the conventions of Bodin and Tengo (2012). Orange nodes are social, with orange social-social edges. Green nodes are ecological, with green ecological-ecological connections. Blue edges represent social-ecological connections.