Participatory approaches and Social Network Analysis to analyse the emergence of collective action for rural development: a case study in the Spanish Pyrenees

Figures & data

Figure 1. The panel a represents the Jacetania comarca (red dot) on the Western side of the Aragonese Pyrenees where the two study areas are located, which are represented in Panel B (villages of Ansó – blue dot – and Hecho – orange dot).

Table 1. Description of the indices used in the structural and positional approaches within SNA (Social Network Analysis).

Variable	Igraph function	Approach	Description
Density	Edge_density	Structural	Ratio between the number of edges in the network and the total number of possible edges. It is an indicator of the level of connectedness among actors. It is expressed as a percentage between 0 and 100, where a high value indicates a high connectedness.
Reciprocity	Reciprocity	Structural	Reciprocity is the tendency of dyads (pair nodes) to have a mutual interaction in a direct network. It is expressed as percentage between 0 and 100, where a high value indicates a high probability of mutual interaction.
Modularity	Modularity	Structural	Propensity of a network to divide into sub-networks or communities. It ranges between −1 and 1, where the maximum value indicates a high propensity to divide into communities.
In-degree	Degree(mode=‘in’)	Positional	Number of edges (links) that point to a node (in-going edges)
Betweenness	Betweenness	Positional	Number of geodesics (shortest paths) going through a node. A high value identifies a node with brokerage position (i.e. strong contribute to manage information exchange within the network)

Table 2. Description of the network and ERGM metrics used in the analysis.

Variable	Statnet term	Attribute type	Description
Edge	Edges	Endogenous	A number of network edges. Its estimate provides information about connection density in the network, where negative values indicate low density. A significant value indicates no random edge formation.
Reciprocity	Mutual	Endogenous	Reciprocity is the tendency of dyads (pair nodes) to have a mutual interaction in a direct network. Positive and significant estimates indicate edge propensity to be mutual (reciprocity presence)
GWESP	GWESP	Endogenous	‘Geometrically-Weighted Edgewise Shared Partnerships’, the propensity to construct a triad interaction among three nodes. Positive and significant estimates indicate the propensity of constructing close triangles or close interactions among nodes. Negative and significant estimates indicate the propensity of constructing open triangles so open interactions among nodes.
Effect of Node attribute	Nodefactor	Exogenous	Effect of node attribute on edge development (in-going and out-going edges); positive and significant estimates indicate a high probability of constructing both in-going and out-going edges
Homophily node attribute	Nodematch	Exogenous	Node propensity to be tied of others of the same category. Positive and significant estimates indicate high node homophily.

Figure 2. The main results emerged from the three focus groups and inductive content analysis.

Table 3. The main characteristics of the actors surveyed. The figures refer to numbers of actors.

Variable	All actors	Farmers	Tourism and commerce stakeholders	Administration stakeholders	Other stakeholders
Actor surveyed	32	18	7	5	2
Age	44 ± 13	44 ± 13	48 ± 11	44 ± 13	34 ± 10
Educational level
Primary school^a	7	7	0	0	0
Middle school^b	4	3	1	0	0
High school^c	5	3	2	0	0
Professional training	8	5	2	1	0
University	8	0	2	4	2

^a6–12 years of age; ^b12–16 years of age; ^c16–18 years of age.

Table 4. General information on the farmers and their livestock activities.

Variable	Unit	All farms
Famers, total	N	18
Employed full-time in farming activities	%	78
Other employment	%	22
Farmers, mean age	years	43 ± 13
LU^a^,b/farm	LU/farm	146 ± 88
LU^a of calves sold/year	N	30 ± 17
Grazing length, months	months	8 ± 2
Owned land, mean	ha/farm	9 ± 8
Rented land, mean	ha/farm	79 ± 239
Communal pastures, mean	ha/farm	356 ± 629

^aLU: Livestock Unit; ^bLU includes cattle and calves.

Figure 3. SNA of the advisory network including all the actors (surveyed and non-surveyed) involved in developing the quality brand. The graph represents the exchange of advice between the actors: nodes represent actors, and links (edges) represent the connections between them (44 nodes, 196 links). The node’s size indicates the in-degree value of the actor (Central actors have the largest values). The network is directional with arrows indicating the direction of advice requests; bi-directional arrows indicate mutual relationships/requests. The colours of the nodes represent the different employment sectors as reported in the legend.

Figure 4. SNA of the trust network of the actors surveyed. F preceding the number indicates a farmer, and O a non-farmer. The size of the nodes in Figure 4(A) indicates the in-degree value of the actor, whereas in Figure 4(B) it indicates the betweenness value given by the other actors in the network (Central actors have the largest values). The colours of the nodes represent the different employment sectors, as reported in the legend. The edges are thicker or thinner according to the average value of trust given by the actors during the survey (26 nodes; 131 links).

Table 5. Nodes, links, structural and positional indicators for the advisory SNA and the trust SNA.

Advisory SNA		Trust SNA
Variable	Results	Variable	Results
Nodes	44	Nodes	26
Links	196	Links	131
Structural indicators		Structural indicators
Density	10%	Density	20%
Reciprocity	53%	Reciprocity	58%
Positional indicators		Positional indicators
In-degree centrality		In-degree centrality
Actor 8, administrator stakeholder	17	Actor 8, administrator stakeholder	12
Actor 24, rural development stakeholder	12	Actor 24, rural development stakeholder	8
Actor 32, veterinarian	12	Actor 6, tourism sector stakeholder	8
Actor 6, tourism sector stakeholder	9	Actor 22, farmer	8
Actor 22, farmer	9	Actor 2, farmer	7
Betweenness centrality		Betweenness centrality
Actor 24, rural development stakeholder	283.5	Actor 24, rural development stakeholder	112.5
Actor 8, administrator stakeholder	268.6	Actor 2, farmer	88.7
Actor 2, farmer	127.6	Actor 8, administrator stakeholder	77.7
Actor 6, tourism sector stakeholder	115.4	Actor 6, tourism sector stakeholder	60.5
Actor 22, farmer	96.2	Actor 22, farmer	58.2

Nodes indicate the number of actors in the network, while links correspond to the number of edges or interactions. Density indicates the connectedness of a network, ranging from 0 to 100. Reciprocity indicates the propensity of mutual interactions between pairs of nodes, ranging from 0 to 100. In-degree centrality indicates the number of in-going links to the node. Betweenness centrality indicates the bridge function of a node. Higher values correspond to stronger contribution to information exchange within the network (dimensionless unit).

Figure 5. Panel A, communities in the trust network identified by the Louvain’s algorithm. Each is indicated by a different colour: community A-red; community B-green; community C-blue; community D-purple. The colours of the nodes represent the different employment sectors while their size corresponds to the betweenness values, according to Figure 4(B); panel B, barplot of employment sectors’ distribution among the communities identified by Louvain’s algorithm; panel C, barplot of educational levels’ distribution among the communities identified by Louvain’s algorithm.

Table 6. Results of the multinomial models to test the variability of the employment sector and educational level categories in function of the Louvain communities.

	Df	Chi Sq	Pr(Chi Sq)	Significance	R^2
Employment sector
Louvain communities	9	22.61	0.007	**	0.37
Educational level
Louvain communities	12	22.34	0.03	*	0.28

Significance is marked by *, corresponding to p-value < 0.05. Pairwise comparisons are reported in table S3.

Table 7. Estimates, standard errors, and z-values for the endogenous and exogenous attributes of the exponential random graph model (ERGM).

	Estimate	S.E.	z-value	Pr(>|z|)	Significance
Endogenous attributes
Edges	−3.7948	0.2736	−13.87	<1e-04	***
Reciprocity	2.4215	0.3049	7.942	<1e-04	***
GWESP^a	1.2231	0.2303	5.31	<1e-04	***
Exogenous attributes
Edges	−4.651	0.525	−8.859	<1e-04	***
Reciprocity	2.175	0.325	6.702	<1e-05	***
Employment sector – Tourism and commerce stakeholders	0.342	0.276	1.242	0.214
Employment sector – Administration stakeholders	1.716	0.352	4.870	0.000	***
Employment sector – Other stakeholders	0.641	0.390	1.641	0.101
Educational level – Secondary school	0.113	0.320	0.355	0.723
Educational level – High school	0.909	0.276	3.289	0.001	**
Educational level – Professional training	0.820	0.280	2.930	0.003	**
Educational level – University	0.352	0.334	1.053	0.292
Homophily Employment sector – Farmers	1.497	0.419	3.574	0.000	***
Homophily Employment sector – Tourism and commerce stakeholders	1.414	0.453	3.126	0.002	**
Homophily Employment sector – Administration stakeholders	−0.282	0.598	−0.472	0.637
Homophily Employment sector – Other stakeholders
Homophily Educational level – Primary school	−0.385	1.009	−0.382	0.703
Homophily Educational level – Secondary school	2.118	0.916	2.312	0.021	*
Homophily Educational level – High school	−1.533	0.973	−1.575	0.115
Homophily Educational level – Professional training	−0.111	0.389	−0.285	0.776
Homophily Educational level – University	0.724	0.427	1.694	0.090	.
ROC^b	0.794

^aGWESP: geometrically-weighted edgewise shared partnerships; ^bROC: receiver operating characteristic curve.

The homophily of ‘OTHER stakeholders’ was not estimated as it had only two nodes. The description of the model terms is reported in table 1 while the pairwise comparisons are reported in table S4. The goodness of fit is reported in Supplementary Figure S1.