El Nino Southern Oscillation (ENSO) is the most significant periodic climate pattern, characterized by sea surface temperature anomaly in the central-eastern tropical Pacific Ocean. It has a substantial influence on global climate patterns due to ocean-air coupling. ENSO episodes have three phases: a warming or El Nino, a cold or La Nina, and a neutral phase. We study ENSO episodes using the near-surface air temperature reanalysis data (1000hPa), considering ocean-air coupling feedback to construct the complex climate network during the onset of ENSO episodes' warm, cold, and neutral phases. The nodes are the geographical sites. The links are made among the nodes based on their similarity above a certain correlation threshold acquired from the significance test for actual climate data and surrogate data.

We visualize the symmetric cross-correlation matrices as heat maps, and the labels of the heat maps correspond to the geographic sites. The middle portion of the heat maps corresponds to the tropical regime, and the upper and lower parts correspond to the northern and southern subtropics. The heat maps of cross-correlation are organized along the diagonals. The parallel lines of the diagonal are the nearest-neighbor nodes correlation, and the off-diagonal patches specify long-range connections, indicating the climate network as a small-world network. During El Nino and La Nina episodes, the adjacent neighboring links are high compared to the neutral condition, which appeared in the middle of the heat maps as the adjacent parallel diagonal lines.

We comprehend the heat maps of cross-correlation with the distance between a pair of nodes, similar to Teleconnection in atmospheric science. We compare the El Nino, La Nina, and neutral phase networks regarding link distribution. We found that during El Nino and La Nina conditions, the neighboring links are higher than the neutral state of ENSO. Consequently, the number of long-range links varies depending on the event's extreme strength.

We exhibit the climate network as a spatially embedded network as well. The collective behavior of the vertexes in a complex climate network shows the signature of three different phases of ENSO episodes and coexisting climatic phenomena along with the El Nino Southern Oscillation response.

We measured the topological quantifiers of the spatially embedded climate network to investigate the event's strength and observed that the long-range links contribute to the event's extreme strength.