1. Supply Chains of Products of Animal Origin: a Complex Network Model for the Strategic Management
Piero Nasuelli, Flavia Clemente
Università di Bologna, DISTAL (Agricultural and Food Sciences Department)
Viale Giuseppe Fanin 50, Bologna, Italia
Remigio Berruto, Patrizia Busato
Università di Torino, DEIAFA (Department of Agricultural, Forestry and Environmental Economics and Engineering)
Via Leonardo da Vinci 44-I, Grugliasco (TO), Italia

2. In a single complex network model the entire frame of animal productions, from the supply chain "Dairy“ (for the milk of Cattle, Buffalo, Sheep, Goat) and from that of “Meat and meat products“ (at the moment Bovine Meat and Pork), 228 nodes and 488 links among the nodes that show the relationships existing between actors , that in this model are the activities, and therefore between an activity of production or processing and the subsequent activity.
Colors:
Rose: Production
Turquoise: Processing
Green: Trade
Blue: Consumption

3. The same network with some groups and subgroups closed
- To distinguish the different descriptive levels are used different geometric shapes: Level1: Rectangle – Level2: Parallelogram – Level3: Hexagon . Level4: Octagon – Level5: Ellipse. - Groups and Sub-groups, which bring together the products of the same categories, are needed in case you wish to calculate the aggregate values.
The same network with some groups and subgroups closed

4. The software used allows different views that highlight different aspects of the network
Here are two different views of the same model of complex network:
- left: the network after the removal of groups and subgroups;
- down: the network for display "Hierarchical from left to right“
In the hierarchical display you can already see the highest density of links characteristic of some nodes in the network, such as 3 turquoise nodes (Segment Transformation) that correspond to the “Packaging through conventional channel”, “Processing into processed products”, and for “possible Losses”, or even 3 nodes in green (segm. Trade) that correspond to the 3 main channels of traditional distribution, ie “HO.RE.CA.”, “Supermarket Chains” and “Retail Sales”.

5. Different layouts that highlight features of the network: Circular Layout, “Custom Groups-Organic Disk”: it highlights the Subnets with some central nodes occupying a strategic position in that subnet

6. Different layouts that highlight features of the network:
Circular layout, “Single Cycle – Organic Disk”: in the center, the most full of nodes, there are the nodes that according to the network structure occupy a more important position

7. The following step: Centrality Measures In adopting from the Physics the definitions of traditioinal centrality measures of complex networks, in our case we have to give an economic interpretation key. Each measure of centrality is useful depending on the circumstances and what aspect of the network and the relationships between the nodes we want to investigate. The definitions, just because now codified, are to "translate" in the economic sphere.
- Degree Centrality: the number of other nodes connected directly to a node, indicator of an actor’s “communication activity”. - Closeness Centrality: the inverse of the sum of distances of a node to others. Thus it measures the distance. A node in the closest position to the other can more efficiently obtain information. - Betweenness Centrality: the portion of the number of shortest paths that pass through the given node divided by the number of shortest paths between any pair of nodes. - Eigenvector Centrality: is a measure of the importance of a node in a network, simply giving a relative score assigned to all nodes in the network based on the principle that connections to high-scoring nodes contribute more to the score of the node in question than equal connections to low-scoring nodes.

8. The end result are new graphics that highlight the most important nodes of this network according to the measure of centrality used for the analysis.
The first thing to point out is that for the moment this is only a quantitative assessment, due to the structure of the model which, however, has been designed keeping us as faithful as possible to the facts
There is not only a single node that can be considered more important than ever, but a group of nodes that are of great importance in a chain of products of animal origin.
The software used for the analysis provides an index for each node in each measure of centrality index whose value is between 0 (minimum) and 1 (maximum value).

9. Degree Centrality: number of connected edges
Ranking:
1: Node Segment Traders, Retail Sales: score 1
2: Node Segment Traders, HO.RE.CA; Node Segment Traders, Supermarket chains : score 0,98
3: Node Segment Processors, Milk S. C., Packaging and Selling trough conventional channels: score 0,69

10. Betweenness Centrality: the portion of the number of shortest paths that pass through the given node
Ranking:
1: Node Segm. Processors, Milk S. C., Pack.&Selling through conventional channels: score 1
2: Node Segm. Traders, Retail Sales: score 0,62
3: Node Segm. Traders, Intermediaries/Agents/Representatives: score 0,61

11. Closeness Centrality: it measures the distance
Ranking:
1: Node Segment Traders, Retail Sales: score 1
2: Node Segment Traders, HO.RE.CA; Node Segment Traders, Supermarket chains : score 0,99
3: Node Segment Processors, Milk S. C., Packaging and Selling trough conventional channels: score 0,92

13. Final Thoughts about the qualitative assessment of the network
clear the importance of the nodes of the segment Trade, both “large-scale trade (supermarket chains)” and “retail sales”, and also the node “HO.RE.CA.”, with some relief for the figure of the “Agents/Intermediaries”.
also evident the importance of the segment of Processors with the Node “Packaging and Selling through Conventional Channels” (note that this network also covers the nodes dedicated to Direct Sales, that has an another node of Packaging), in these first 3 positions only for the Milk Supply Chain, but among the first 7 positions also appears the node “Packaging & Selling Through Conventional Channels” related to Meat Supply Chain.
another recurring node among the first 7 positions of the rankings of centrality measures is the node “Slaughterhouse Waste destined for Rendering” related to Meat Supply Chain.

14. Conclusions These 3 rankings according to the 3 measures of centrality for the moment do not take into account the importance, the weight, of the relationships between the various nodes. We can say that now the network is not "weighted“. The weight of relations in the network can change the ranking.
…and certainly would have this effect for some of the nodes that currently have an high place in the rankings only by the number of nodes in the network to which they are connected in a direct manner (Node Retail Sales, for example, connected with a very high number of nodes in a direct manner, but it is thought will prove to be much less "heavy", less important of Node Supermarket Chains).
…therefore the next step will be define what the meaning by an economic point of view of each of the centrality measures, giving them an economic key to reading
…and of course to weight the relations of this complex network.

15. Thank you for your attention
Piero Nasuelli, Flavia Clemente
Università di Bologna, DISTAL (Agricultural and Food Sciences Department)
Viale Giuseppe Fanin 50, Bologna, Italia –
Remigio Berruto, Patrizia Busato
Università di Torino, DEIAFA (Department of Agricultural, Forestry and Environmental Economics and Engineering)
Via Leonardo da Vinci 44-I, Grugliasco (TO), Italia –